The canonical formalism for general relativity on a null surface is compared with that on a space-like surface using Ashtekar variables, the self- dual connection and a densitized triad. The principal difference lies in the appearance of second class constraints. These arise in part because the metric on a null surface is singular, in part because on a null surface there is a preferred direction, and in part because a compact mapping will not map a null surface into a null surface. Second class constraints are eliminated by the use of Dirac brackets. It is shown that, in principle, this is particularly straightforward in this case.

PACS numbers: 04.20.Fy