In I 1 1 we studied the existence and uniqueness of solutions to the following typical stochastic integral equation with respect to semimartingalesThis paper is devoted to the existence and uniqueness of solutions to the following delay stochastic integral equationwhere Xd=(Xd(t)) is said to be the delay process of X defined as follows:in whichis a continuous functionsatisfies some conditions. We should point out that our results can be generalized to the more general equationwithout any difficulty, where X and Xdare n-dimensional stochastic processes andsemimartingales