India, which has over 100,000 Tibetan refugees, has been seen as one of the potential flashpoints on the route of the Olympic torch.
Thousands of police have been deployed in Delhi for the relay, especially along the route of the Rajpath.
There were complaints from some locals, trying to go about their daily business, over the inconvenience caused by the tight security.
Earlier the Olympic flame had arrived by plane from Pakistan, on the latest stage of its worldwide tour.
Some Tibetan protesters waved flags from police vehicles after being detained outside the airport.
Protesters shouted slogans such as 'Long live the Dalai Lama' and 'Stop the killings in Tibet'.
Exiles objecting to China's treatment of Tibet have been holding protests across India for several weeks.
After Delhi, the torch relay goes to Thailand, Malaysia and Australia, before reaching China on 4 May, having travelled 137,000 km.