The grizzly bears appeared when we were least expecting them.

One moment we were drifting down a gorgeous blue-green river of glacier meltwater and enjoying the warm sunshine, the next one of our companions shouted: “Bears!”

And there they were – a mother grizzly and her two cubs bustling along the riverbank.

Grizzlies are killing machines – they can rip you to pieces, they can run faster than a man and they can climb trees.

But we were separated by a stretch of water – although they can also swim – and this beautiful but deadly animal was not interested in us. Casting maternal glances over her shoulder, she led her adorably cuddly offspring in search of a meal of salmon.

It was a magical moment on a holiday that was like stepping into a wildlife documentary.

As we drifted down the Kenai river, bald eagles kept their beady eyes on us and thousands of spawning salmon swam beneath us in the chilly, clear waters.

A holiday to Alaska really is the journey of a lifetime, especially if you combine a land tour with a cruise. We spent the first week of our Princess tour travelling through the vastness of Alaska’s interior, with every day bringing a new memory to last a lifetime. Then we spent another week on board the Coral Princess cruise liner, exploring the stunning coast with its teeming wildlife, and watching glaciers tumble into the sea.

We flew to Anchorage to join our escorted tour party on a day of almost supernatural clarity. Our guide pointed out Mount McKinley, at 20,000ft the tallest peak in north America – it was a staggering 280 miles away.

You learn to treasure such days in Alaska – in the short summers the weather can sometimes be warm and welcoming, but the next day the rain may lash down.

Princess operates a number of lodges in Alaska and we spent our first few days on the beautiful Kenai peninsular. You stay in delightful wooden cabins – each with its own wood-burning stove.

The lodge comes to life for the Alaskan summer and is then mothballed for the long, dark winter, leaving the countryside to the tough local residents.

The sun had given way to grey skies and mist when we travelled from Kenai to the port of Seward for a day-long cruise around the Kenai Fjords National Park.

In a few short hours our breath was taken away by the wildlife – humpback whales emerging out of the mist to dive in front of our boat, lolling seals, angry sealions, even mating sea otters.

And then the air temperature suddenly plunged and out of the mist loomed the Aialik Glacier.

No photograph or high-definition television picture can truly represent the majestic beauty of a tidewater glacier as it flows into the sea. The Aialik Glacier towers higher than St Paul’s Cathedral and on days when the weather is overcast a trick of the light turns it breathtakingly blue.

Ships and icebergs do not mix – ask the captain of the Titanic – but ours was expertly piloted to the very edge of the floating ice at the foot of the glacier, so that the towering wall was about a quarter of a mile away.

The captain cut the engine and we simply watched and listened to the cracks and booms as pieces of ice the size of a house broke away and tumbled into the sea.

Next stop was the Denali Princess Wilderness Lodge, which is right on the boundary of the national park that is home to Mt McKinley. We had travelled north and the summer was ebbing away to be replaced by a stunning display of autumn colours.

It was here that we flew in a helicopter over the glowing autumn landscape to land on a glacier.

Another day we clambered on to a school bus and a National Park guide drove us through the park on the lookout for wildlife. Suddenly, there was a a huge moose – in the mating season they are as dangerous as bears, so we watched from a distance.

Then it was time to head for our ship and we boarded Princess’s special train, which trundled all day through beautiful countryside to the port of Whittier, where the Coral Princess was waiting.

It carries just over 2,000 passengers and has the sort of jump-to-it service Americans demand, but there’s plenty to keep you amused.

But although life on board is comfortable, this holiday is all about the destinations.

And for a marvellous week, the Coral Princess made its way down the coast of Alaska towards its final stop at Vancouver.

For many people the highlight of the voyage will be the visit to the Glacier Bay National Park, where glaciers crash into the sea, waterfalls cascade down rugged mountains and bears roam the shores.

Then there were the whales. One of our ports of call was Juneau, Alaska’s capital that can only be reached by air or sea. On board a little tour boat, we headed off in search of whales.

We sailed past several humpbacks, but didn’t stop because one of nature’s most amazing spectacles was taking place further on.

There were ten humpback whales hunting together circling a shoal of fish and creating a “net” of bubbles to trap them.

When the moment is right the huge whales rush to the surface, scooping thousands of tiny fish into their jaws. Even the crew and our naturalist guide just stood and watched in silence as the drama played out in front of us.

Yes, Alaska is an amazing place.