But the mountain gorillas in the mist-covered hills around Bwindi, a short flight from the country's main airport, Entebbe, are the main attraction. There are thought to be only about 880 mountain gorillas in the world, divided between Uganda, Congo and Rwanda. About half live in Uganda.

Some wildlife enthusiasts with whom I trekked into the forest had come to the country solely to see the gorillas. It's not cheap - a one-day permit to trek into the hills and observe the gorillas costs US$500 - and it's not easy to reach them. But the experience is worth the effort.

I start out early from Mahogany Springs, an elegant boutique lodge on the edge of the small tourist town of Bwindi, and gather with travellers at the park headquarters. The mist is still thick over the tree-covered hills. Agenya David, Bwindi's park ranger, provides a briefing. We're instructed to keep a minimum of seven metres from the gorillas at all times, for their safety more than ours, and anyone with a cold or infectious diseases is encouraged to postpone their trek.

The health and safety of the rare gorillas is taken seriously. So is ours: rangers carrying AK-47s accompany groups on all treks.

My group is allocated the Mubare family of gorillas. Reaching them will involve several hours of trekking. We set off into the cool, musty forest, which warms rapidly as we climb. The forest is almost impenetrable, with dense undergrowth and sprawling trees. Three L'Hoest's monkeys scatter as we approach.

It's a tough, sweaty trek up and down hills; some of us struggle with the pace and heat. Parts of the path are wet and slippery, others grown over. Obed, our guide, machetes branches out of our way and we continue through. All the time, the forest is full of the musical clicks and whistles of birds and insects.

We talk about the complicated relationship between people and the gorillas here. Ever since the days of Dian Fossey, the scientist, conservationist and author (played by Sigourney Weaver in the film ), who fought to protect Uganda's disappearing mountain gorillas from poaching and other dangers, there's been debate over whether gorilla tourism is a good thing. Fossey opposed it because humans bring diseases that can spread to the animals, as well as disturbing the gorillas in their natural habitat.

But gorillas also bring needed money to this poor region of Uganda. The local community receives 20 per cent of the US$500 permit fee. Then there are the jobs: rangers, porters, trackers, staff at hotels, and restaurants and drivers.

The WWF estimates each gorilla brings in up to US$1 million in revenue for Uganda each year. That money is also used to protect the gorillas, reducing poaching (gorillas aren't hunted, but poachers set snares for other animals, which injure the gorillas, sometimes fatally) and buying land that would otherwise be used for farming, which swallows up their habitat. One of the big successes is persuading local people of the value of gorillas - far better alive than dead. Numbers of the critically endangered animal have been steadily rising.

I ask Dr Fred if he thinks gorilla tourism is a problem for the animals. "Not at all," he replies, firmly. "But that has a lot to do with all the rules." Tourist numbers are strictly limited to six per group. Of 31 gorilla groups in the area, only 11 are visited a maximum of once per day, and viewing is limited to one hour to reduce stress.

To help find the gorillas, expert trackers go out in the morning to locate the moving groups. A few hours into our hike, Obed starts to listen attentively for sounds. He follows signs left by the trackers; a small, almost imperceptible clue, like the direction of a broken branch, points him to where they and the gorillas are. He listens again and our trackers call us to them.

I catch my first glimpse of a female gorilla among the bushes. She's in the shade under branches, lying on the ground on her back, chewing the leaves off twigs and broken branches. When she's finished, she lumbers off to look for more.

We then find the silverback, Kanyonya, leader and protector of the group, recently "promoted" after the death of the previous alpha male. Most of our hour is spent with him, watching him eat ginger or laze about on his enormous back. His features are lit by the bright sun. Sometimes he looks at us, but mostly he goes about his own business. The guides grunt - an imitation of the gorillas, a noise that puts the gorillas at ease.

Many people talk of the human-like features of gorillas and their expressive eyes. But what impresses me most is Kanyonya's size and power. His enormous head looks like it would be impossible to lift. His body, shoulders, back and legs are all massive. He's still quite young, too, with plenty more growing to do.

We observe four gorillas from the Mubare group. Obed tells us that the group is growing: "Three weeks ago, the silverback, Kanyonya, fought the silverback from another group, Rushegura, and snatched a female, Kyirinvi. She's now part of the group and will help him breed and make a bigger group."

Kanyonya bears the scars of the fight. "He fought hard to snatch this female," says Obed. It's not the first time he's fought - another female in his group was also snatched.

Thunder rolls across the hills. I've been busy taking photos and the hour has passed in a flash. I put my camera down and enjoy the experience of being among the gorillas for a while. The big shoulders of the silverback disappear into the forest.

This time, we don't follow, but leave him in peace. A medium-sized female gorilla called Twesiima comes out of the undergrowth, catching me by surprise, and saunters indifferently by.

It starts to rain hard as we hike up and over a high ridge, leaving the fertile green hills and the mountain gorillas behind in the mist. It's good news that their numbers are on the rise - previously, many expected them to become extinct. But this isn't a time for complacency, says Dr Fred, as we descend to the village.

"They're still considered critically endangered. The total hasn't had a big multiplication effect. It's not a huge difference. Maybe if they had doubled or tripled, we could start to think about adjusting the term 'critically' endangered. But we have to keep maintaining this balance."