In this paper we study a class of two-parameter backward stochastic differential equations driven by a Brownian sheet. We show the existence and uniqueness of a pair of 1-adapted processes {(Y z ,Φ z );z∈R z 0 } which solves the following equation where W={W(z);z∈R z 0 } is a Brownian sheet on a complete probability space (Ω, F, P) and R st is the rectangle [0, s]×[0, t].