Abstract: Let D \subset \mathbbR_+^2 be an open set with pieeewise smooth boundary.It is shown in this papor that the germ lévy’s Markov property holds for two-parameter Markor processes defined in1.Furthermore,if D is a union of rectangles,the sharp léry’s Markov property is also satisfied.These extend the corresponding results in1for bounded and convex-type set D and that in2for Brownian sheet.