But, since the recent disastrous flood that left the park under 18 feet of water, there is no place left in the park for a rhinoceros to stand; and there is no food left for them to eat. Those that have not drowned or been swept away have fled.
I was being driven along National Highway 37, the road that skirts the south of the national park, when I first set eyes on one of these giant refugees. We rounded a corner and a big lorry was parked in the middle of the road. Not stalled: parked, with deliberation.
No more than 30ft ahead was a large rhinoceros, standing in the middle of the road. Beyond, other lorries had stopped, and the huge animal's prehistoric form was silhouetted in their headlamps. Exhaust fumes swirled around it. It was a vision out of an apocalypse. A few minutes later the animal trundled off the road and into the trees on the verge and we continued on our way.
The rhinoceros on the road is an emblem of the immense crisis Kaziranga National Park confronts. This is one of the most important and also one of the most successful wildlife reserves in the Indian subcontinent.
But thanks to this year's floods, which continued for three months, Kaziranga has effectively been turned inside out. The pride of the park - the 1,164 rhinos, 80 or so tigers, the thousands of swamp deer and hog deer on which the tigers prey, the water buffalo - all have been forced to flee.
Within the park, much of the infrastructure painstakingly put together by 500 guards and rangers has been smashed to pieces or washed away: lookout camps, wooden bridges, earth platforms constructed to give the animals a place to retreat - all battered or broken.
Kaziranga's tragedy is particularly poignant because this is a park that has been bucking the odds. The crisis of India's parks and reserves is perennial, and perhaps inevitable. An exploding human population continually threatens to encroach on land reserved for wild animals.
Public money to fund the parks is frequently siphoned off by corrupt politicians, leaving the parks gasping for the bare essentials, such as fuel for the jeeps in which the gamekeepers patrol. Salaries can remain unpaid for months. Tempted by the astronomical value of rhino horn in the Far East, where it is an ingredient in traditional Oriental medicine, ruthless, heavily armed poachers are a constant menace.
Two years ago, Kaziranga was in acute crisis. The park depends on a large team of working elephants and all were visibly suffering from malnutrition, and three were suspected of having TB.
The problem was that money promised by the state government was simply not arriving. The park was surviving on credit. Hundreds of thousands of rupees was owed for fuel. The guards, who earn pounds 12 a week, had not been paid for months. For want of such pitifully small items as torch batteries, night anti-poaching patrols were sometimes unable to do their work.
As a result of an article in a British magazine describing the park's plight, which evoked a generous response, the situation two years on is in many respects much improved. The ancient, disintegrating off-road cars were augmented by neat little Suzukis. Motor boats were bought for patrolling during the monsoon. Much money has been spent on infrastructure. Often there has been no money to maintain or fuel the new cars and boats. But the morale of the park's 500 staff, which even amid the crisis two years ago was strikingly high, remained impressive.
Now Kaziranga is almost back to square one.
Divisional Forest Officer P S Das spelt out the scale of Kaziranga's new disaster. "We've found 31 rhinos drowned so far - one drowning calf was rescued. There may well be more drowned carcasses: the full picture will emerge in 15 or 20 days, when the water has receded further; 30 to 40 camps out of 100 have been destroyed. We've lost 21 timber bridges. Sixty-eight of the earth platforms have been damaged, by the animals, the flood or both. There are 100 kilometres of good, driveable road in the park which will need to be cleared and repaired. All of this will take a lot of money, which we don't have."
He added: "We haven't slept for two weeks."
Apart from all the work of putting the park back together again there is also the looming danger of an eruption of opportunistic poaching.
In the past four years, Kaziranga's guards have had great success in containing poachers. During the Eighties and early Nineties, nearly 35 rhinos per year were murdered in the park for their horns. Since 1994, that average has been reduced to fewer than 13 per year. Until the monsoon, only one rhino had been lost to poachers this year.
But with the park in its present disarray, the poachers are coming at the animals thick and fast. Mr Das recounts four incidents in the past two weeks. "The day before yesterday we killed two of them," he said, matter of factly. "We have no regrets about killing poachers, because if we didn't kill them, they would kill us."
With Kaziranga under water and the animals scattered across the countryside, the danger has never been greater. Mr Das is not particularly anxious about the tigers. "They are very good swimmers and they are very agile, very good at saving themselves. They are also extremely difficult to poach. Tigers have not been poached at Kaziranga for years."
The rhinos are a different matter. "The rhinos are good swimmers, too, but now they are hungry and weak. A rhino needs 80 cases of grass per day. The grass in the park has been ruined."
Now the desperate rhinos are all over the area - up in the Mikir Hills to the south of Highway 37, blundering through tea gardens. "Thirty to forty," said Mr Das, "are in a small area at the western extreme of the park."
It was at exactly that point that I had seen the rhino on the road, days before. Some days later, on the journey back to Guwahati, I saw five more at the same spot. All five were very dead, beached in a still-sodden field half a mile to the north of the highway. Birds were feasting on the carcasses.
Later that day, Assam's chief minister, Prafulla Mahanta, announced that his government was releasing 5 million rupees (pounds 70,000) "forthwith" for the repair of roads, bridges, earth platforms and camps within the park.
What he omitted to say was that most of this sum was not an extra grant but money long owed to Kaziranga by the state government, and long held up. Kaziranga's unequal struggle goes on.
n An India-based charity working to restore Kaziranga National Park is The Rhino Foundation, c/o Tollygungge Club, 120 DP Sasmal Road, Calcutta 700-033, India; telephone 00-91-33-473-3306.