Florida's Everglades National Park

Without our blue earmuffs, the noise is appalling: a huge, throbbing shriek. A startled heron rises from the reeds as we approach, wide grey wings beating a hasty retreat from the oncoming cacophony. It makes our declared intention of sneaking up on an alligator seem ludicrous. Maybe we'll surprise a very old, very deaf, very bored one. Maybe.

Riding on an airboat in the Florida marshlands looks great in principle. Flat-bottomed skiffs are propelled across water, reeds and mud by a 6ft fan bolted on to the back - a hovercraft without the girly skirt. The driver sits on a high frame that commands a view of the flat landscape, and we passengers sit in front. The only problem is that the fan, which whirrs away gently at low velocities, hits an ear-shredding pitch when we reach our top speed of 45 miles per hour.

Which is where the blue earmuffs come in. It makes for a strangely solitary experience, sitting as you are among your fellow travellers, but unable hear them and, in turn, to speak to them. So you have to keep your eyes open. It's the bird life that you notice first: moorhens, cranes, the odd raptor wheeling overhead. Then insects: electric blue dragonflies an inch long, flitting about our ankles. Then, of course, there's the landscape itself, which is dead flat - a tropical East Anglia lurking under a bright blue sky. And then ...

No alligators yet. Richard, our "boat captain", had brusquely informed us about the safety features on his vessel as we'd sat down: "I've got life jackets under the seats; there's a fire extinguisher at each end of the boat. I've also got a cellphone in the locker in case we get into trouble." It didn't seem to have occurred to him that staying in a burning boat might be preferable to diving into alligator-infested water, with or without a life jacket. In either case, it was hard to see how a mobile phone was going to help us out.

Still, we needn't have worried. We'd clearly spooked all the available alligators for today, although that didn't make the waters around the boat look any more inviting. The area we'd set off from, half an hour by road to the south-east of Orlando, is called Boggy Creek - and it lives up to its name. Whether clogged with pondweed or washing up against tangles of muddy roots, the scenery looks primordial: the sort of sludge that you could imagine the dinosaurs rising up out of aeons ago. Boggy Creek itself is part of the Central Florida Everglades, the area of sub-tropical wetlands that extends from Orlando to the southern tip of the Florida peninsula. This vast, slow-moving basin of shallow water, the result of seasonal overflow from the River Kissimmee and Lake Okeechobee, is essentially a swamp, a place of mangroves, reeds and sawgrass. And, apparently, tens of thousands of examples of Alligator mississippiensis. All of whom, it appeared, were currently out at lunch.

Then two things happened in quick succession: Richard cut the engine and we saw our alligator. Now, there's a perfectly sensible school of thought that says one should always keep the motor running when one startles a man-eater, but Richard seemed to know better. It was about 8ft long, he informed us in the awkward silence that developed as we floated, blue earmuffs discarded, alongside the beast. "The best way to tell is to measure the length in inches from the eyes to the end of the nose, and that's the length in feet. It's not scientific" - here his Florida drawl grew more pronounced - "but I've got a tape measure here if you want to test it out."

Ho, ho. Nervously, we watched the alligator, and he, for Richard assured us it was a male, watched us from his muddy outpost. Alligators can live for 30 to 40 years, and they seem to be more engineered than evolved: precision fauna, built like military hardware. Camouflage is standard, with a long row of green spikes down the spine, and the gun turret of its snout completing the impression of cold, calculating menace. Our strengths and weaknesses were no doubt being analysed, and a tactical strike would be launched should we stray too far into enemy territory. Those teeth looked armed and dangerous.

Nevertheless, the tourist imperative swiftly overcame us and we seized our moment, cameras clicking and flashing. Alligators make excellent subjects for photography: they don't blink at crucial moments, and red-eye is their natural state. They also stay impressively still throughout the process, reducing the effects of camera shake (unavoidable, given the circumstances). Indeed, so rigid was our reptile that suspicions began to be raised among our company that Richard might have planted a decoy. Was this, we wondered, the real deal, or just a cardboard croc? Our alligator twitched in annoyance. There we were, in the middle of nowhere, staring at a predator whose ancestors had enjoyed millions of years at the top of the food chain. Had we no respect? Even the dragonflies suddenly seemed to have urgent business elsewhere. Then, without so much as a toothy yawn, the alligator slid into the water, a serrated tail leaving ripples on the surface.

Perhaps he'd gone below, in preparation for an attack. "They can jump about three and a half feet into the air from water," said Richard, not altogether reassuringly. He, after all, was safe in his high chair. The ripples from a few lethargic wavelets slapped the side of the boat. Some more - slightly panicky - silence ensued. But no, we'd been spared. Even tooled-up reptiles know that some battles aren't worth the bother.

Encounter over, Richard gunned the engine. It seemed that we'd survived without having to resort to his cellphone. The waters, he said, were too high for it to be likely that we'd see many more 'gators on our return journey, so he contented himself with showboating the skiff on long swoopy corners round the waterlogged channels. Back at Boggy Creek HQ, one of the airboats moored alongside ours at the jetty was called Gator Terminator. (Controlled hunting has been legal in Florida since 1987.) Somehow, it didn't seem likely that our alligator, silent but deadly, would be too worried.

Boggy Creek Airboat Rides (001 407 344 9550; bcairboats.com), 2001 East Southport, Orlando, Florida runs alligator-spotting trips. Half-hour rides cost $19.95 (£11) for adults and $15.95 for children. A cab from downtown Orlando costs around $50. Virgin Holidays (0871-222 1232; virgin.com /holidays) offers a seven-night fly-drive in Orlando from £459 per person. This includes return flights from Gatwick or Manchester and a week's car hire