"Wow," one of them said, "are you famous or something?"
Er, no, was the obvious reply. I'm your next-door neighbour. You cannot be famous if nobody has ever heard of you which, thankfully, American television viewers largely had not.
But the strangest things have begun to happen since the BBC set up World Service Television, the televised equivalent of BBC World Service radio. It is an unsung hero for Britain, a prophet without honour in its own country because you cannot see it here unless you have a special satellite dish. The fame it brings abroad is decidedly peculiar. A few months ago I was in a hotel in Oman, on the edge of the Persian Gulf, having a row with my four-year-old son who was far more interested in going for a ride on a camel than eating his lunch. In the middle of this father-son macho stubbornness a man in Arab dress tapped my shoulder.
"Excuse me," he said, shaking hands, "your name is Gavin Esler, isn't it."
"Um, yes," I admitted, while trying to stop my son from smearing me with discarded humus. "How do you know?"
"I see you on television."
"You do? Where?"
"Abu Dhabi. Dubai. Bahrain. Here in Oman. BBC World."
He explained he was a businessman who travelled widely in the Middle East where BBC TV is extremely popular. He watched it at home and in most international hotels - including the one in which we were staying. On another occasion I was in a shopping centre in Malaysia, again trying to restrain my children who wanted to buy cheap "Walt Disney" videos which looked decidedly home-made. It always seems to be at such moments of inglorious paternal stress that someone from the crowd decides to recognise me.
While I was prizing "Hercules" from four-year-old hands a Chinese couple politely began asking if I had come to Malaysia to report the collapse of the currency. I was unshaven, sweaty, grumpy, all the things a father is supposed to be on holiday, and not much in the mood to discuss BBC coverage of the Asian economic crisis, but what can you do?
"No, I am not reporting on it," I answered, "but I am benefiting from it. Everything here is very cheap."
The couple said they were viewers of BBC World and discussed at length the respective strengths and weaknesses of our TV coverage compared with that of CNN. Even more strange (if that is possible) my appearances on BBC World reunited me last month with an old friend I had not seen for almost 20 years. The friend, Mike, had emigrated to Africa and we lost touch. I always suspected he would end up in jail, featured in the Sunday newspapers or - and this was a long shot - very, very rich. Last year he sent me a letter from Johannesburg and renewed our friendship. He returned to England for a visit in April and we met for the first time since the 1970s. I cannot tell you how much joy that meeting gave me, or his stories of making a fortune in diamonds, property and wineries. But if he had not spotted me on BBC television in South Africa, I would never have heard from him again.
Now all this could be ego massage, especially since the audience for our new British service News 24 is, shall we say, still growing. It is six months old and will be available only to cable and satellite subscribers until the new digital terrestrial technology becomes available this autumn. But these disconnected anecdotes demonstrate how the world is becoming an information village in a way none of us could have guessed a few years ago.
A Jewish friend who lives in New York was watching CNN during the Gulf War when she saw a (fortunately incorrect) report that Tel Aviv had been hit by an Iraqi gas attack. She immediately tried to phone her mother in Israel. The line was busy. When she eventually got through it turned out she had been beaten to the call by another relative who was living in Brazil. Thousands of miles apart, they had been watching the same television news report, and had taken the same action of calling home.
At Christmas 1997 a group of Tupac Amaru terrorists held dozens of Japanese diplomats and other guests hostage in Peru. I flew to Lima and transmitted live and pre-recorded reports every few hours back to London. Then I returned to my hotel room and watched those same reports bounce back to Lima on another satellite within minutes.
There are Marshall McLuhan's profound implications about all this - Global Village, that kind of stuff. But the most obvious implication struck me on a flight back to London from Asia with my wife. I chatted amicably to someone on the plane who asked all kinds of informed questions about programming on BBC World television. At the end of the discussion the man turned to my wife.
"And," he said, "what do you do, Mrs Alagiah?"
Gavin Esler is a presenter on BBC News 24 and on BBC World Service Television. His book `The United States of Anger' is published by Penguin this month.