Pronghorn antelope all but outnumber people in wide-open WYOMING , the ninth largest but least populous state in the union, with just 460,000 residents. Above all, this is classic cowboy country - the inspiration behind Shane, The Virginian and countless other Western novels - where the days of the open range are evoked by rodeos, country-and-western dance halls and ranchwear stores. The state emblem, seen everywhere, is a hat-waving cowboy astride a bucking bronco.

Northern Wyoming is the prime tourist goal, with well over three million per year heading for the simmering geothermal landscape of Yellowstone National Park , and the craggy mountain vistas of the adjacent, and equally outstanding, Grand Teton National Park . Wedged in between Yellowstone and South Dakota to the east are the helter-skelter Bighorn Mountains , likeable Old West towns such as Buffalo , and the otherworldly outcrop of Devils Tower .

The meager supply of buffalo in early Wyoming caused fierce intertribal wars over hunting grounds and kept the Native American population down to around 10,000. However, Sioux, Cheyenne and Blackfoot combined to inflict notable defeats on the US Army before it could clear the way for pioneer settlement in the 1870s. The cattle ranchers and sheep-farming homesteaders who followed engaged in violent range wars over grazing rights to the wiry grasslands.

Unlikely as it may seem, this rowdy, heavily male-dominated state was the first to grant women the vote in 1869 - a full half-century before the rest of the country, on the grounds that the enfranchisement of women would attract settlers and increase the population, thereby hastening statehood. A year later Wyoming appointed the country's first women jurors, and the "Equality State" elected the first female US governor in 1924.

The absence of rivers to irrigate farmland has effectively put a lid on agricultural and population growth. These days, any weather-beaten, denim-clad stranger is more likely to be an oil roustabout than a genuine cowboy, fuel and mineral extraction having replaced livestock as the mainstay of the economy in the early part of the twentieth century.  TOP

Grand Teton National Park and Jackson Hole
The classic triangular peaks of GRAND TETON NATIONAL PARK , which stretches for fifty miles between Yellowstone and Jackson, are every bit as dramatic as the mountains of its congested neighbor, and a visit should be more than an afterthought on the route south. Though not especially high or extensive by Rocky Mountain standards, these sheer-faced cliffs make a magnificent spectacle, rising abruptly to tower 7000ft above the valley floor. A string of gem-like lakes is set tight at the foot of the mountains; beyond them lies the broad, sagebrush-covered Jackson Hole (a "hole" was the pioneers' term for a flat, mountain-ringed valley), broken by the winding Snake River.

The Shoshone people knew the mountains as the Teewinot ("many pinnacles"), but their present name, meaning large breast, was bestowed by over-imaginative French-Canadian trappers in the 1830s. After Congress set the mountains aside as a national park in 1929, it took another 21 years of legal wrangling for Grand Teton to reach its current size - local ranchers protested that the economy of Jackson Hole would be ruined if further land was surrendered to tourism. Meanwhile, John D. Rockefeller Jr bought up a large swath of Jackson Hole and presented it to the government for free (on the condition that the Grand Teton Lodge Company, which he then owned, would be the exclusive operator of park concessions).

No road crosses the Tetons, but those that run along their eastern flank were designed with an eye to the mountains, affording stunning views at every turn. Two excellent side trips are the Jenny Lake Scenic Loop , leading to a face-to-face encounter with towering, partly hunchbacked Grand Teton Mountain , and the narrow track up Signal Mountain , which gives a fine view of the five main Teton pinnacles and Jackson Hole.

Hiking trails, too, have been laid out so that no time is wasted in getting to the highlights. One easy and popular walk is along the sandy beaches of Leigh Lake , where the imposing 12,605ft Mount Moran bursts out dramatically from the lake shores. Also very accessible are the cascading Hidden Falls , reachable by a two-mile walk along the south shore of Jenny Lake; it's also fun to take the shuttle boat ($5 round-trip) across the lake, and walk the remaining 800 yards. For the more adventurous, the rocky nine-mile trail from Hidden Falls through U-shaped Cascade Canyon leads to aptly named Lake Solitude . Another strenuous hike, and an excellent way to reach the tree line in a short distance, is the five-mile trail from Lupine Meadows , just south of Jenny Lake, which skirts small glacial pools like Amphitheater and Surprise lakes.

On the flat roads of the Hole, cycling is a joy; rent a bike down in Jackson ($25-30). To admire the Tetons from water , take a float trip along the Snake River or rent a rowing boat from Colter Bay or Signal Mountain marinas ($25). In winter, all hiking trails are open to cross-country skiers , and snowmobiles can be rented from various outlets in Jackson. Excellent rock climbing opportunities exist within the park. Contact the Jenny Lake Visitors Center (tel 307/739-3343) for climbing details. Climber's Ranch , within the park on Teton Park Road , has basic dorm accommodation for climbers only (June-Sept only; tel 307/733-7271; $7).

Northwest and North Central Wyoming
Northern Wyoming has a lot more to offer than just a handy route between the Black Hills and Yellowstone. The surreal volcanic monument of Devils Tower , the abrupt Bighorn Mountains and the desertscape of the Bighorn Basin are the major natural attractions in a land steeped in the history of Native American wars, outlaw activity and pioneer hardships. Small towns such as unassuming Buffalo and the more commercialized Cody , developed by Buffalo Bill himself, are potential stopovers.

South and Central Wyoming
State capital Cheyenne is the only town of real note in the lower two-thirds of Wyoming. Set in the heart of rich prairie - a surprise after the scrubland, mountain and desert of most of the region - it has closer economic ties with Omaha or Denver than with the rest of Wyoming, a point the more northerly oil city of Casper stressed in its unsuccessful bids to become the seat of government. West of Cheyenne, smaller Laramie possesses an agreeable frontier feel, while the spectacular wilderness of the Wind River Range , accessible from Pinedale and Lander , accounts for most of the west central portion of the state.

Yellowstone National Park
Millions of visitors each year come to YELLOWSTONE NATIONAL PARK , America's oldest national park and the largest in the lower 48 states, to glory in its magnificent mountain scenery and abundant wildlife, and above all to witness hydrothermal phenomena on a unique scale. Measuring roughly sixty by fifty miles, and overlapping slightly from Wyoming's northwestern corner into Idaho and Montana, the park centers on a 7500ft-high plateau, the caldera of a vast volcanic eruption that occurred a mere 600,000 years ago. Into it are crammed more than half the world's geysers , in which the rain and snow that seep through the bedrock escape the pressure-cooker conditions under the surface in intermittent spectacular blasts, plus thousands of fumaroles jetting plumes of steam, mud pots gurgling with acid-dissolved muds and clays, and hot springs.

Yellowstone amounts to an extraordinary experience, combining the colors of the Grand Canyon of the Yellowstone, limpid Yellowstone Lake, the wild flower meadows and the rainbow-hued geyser pools; the sounds of subterranean rumblings, belching mud pools, and steam hissing from the mountainsides; and the constant smells of drifting sulphurous fumes, with the presence of browsing bull moose, shambling bears, heavy-bearded bison, herds of elk and ubiquitous scurrying marmots . It is, however, very popular; if you let yourself get frustrated by the inevitable crowds and expense, you risk missing something very special. The key to appreciating the park is to take your time, and to plan carefully; above all, try to allow for a stay of at least three days.

 All of Yellowstone's major sights are labeled and signposted within a few hundred yards of the 142-mile Loop Road , a figure-of-eight circuit fed by roads from the five entrances. Although the speed limit is a radar-enforced 45mph, the traffic makes journey times hard to predict. To get the most out of a visit, even if you're short of time, choose one or two areas to explore thoroughly. Only in the early morning is cycling bearable or safe; there are no mountain bike trails. Though you can expect to walk considerable distances along the canyon and geyser trails, it's worth leaving the backcountry hiking for the more scenically rewarding Grand Teton National Park.

The following account runs clockwise around the Loop Road, from Old Faithful to the Yellowstone Lake area, both of which lie in the southern reaches of the park.  TOP