Let BH ={BH(t), t ∈ RN+} be an (N, d)-fractional Browniau sheet with Hurst index H =(H1,H2,...,Hd).We study the existence and the regularity of the selfintersection local times of BH and establish the sharp local and uniform Holder conditions for the self-intersection local times.We also determine the Hausdorff dimensions of the set of multiple times when they are not empty.The main tool we use here is the newly developed sectorial local nondeterminism of fractional Brownian sheets.This talk is based on joint works with Mark Meerschaert and Yimin Xiao.