A note on intersections of S-branes with p-branes

We first investigate intersections of an S-brane with a single p-brane and show that in addition to the already known solutions, it is possible to place the S-brane so that the radial part of the p-brane is not included in its world volume. This leads to a new set of solutions. Second, we consider intersections of an S-brane with a supersymmetric Dp(1)-Dp(2) intersection and find the list of allowed solutions for both positions of the S-brane. Among them there are D1-D5-S1 and D1-D5-S5 intersections which might be appropriate for studying time dependent AdS/CFT correspondence.