In this paper, we introduce a class of generalized Browaian sheets and extend the OUP; in [1]. By studying some fundamental properties of the former process, we first derive some of simple relaxed past Markov properties of the rwo processes. Next, utilizing the relation between the two processes, we successively prove that, for two kinds of general sets, they possess the general relaxed past Markov properties and the Levy Markoy properties re-spectively. As a result, we conclude that the OUP; in [1] also has general Markov properties for the corresponding sets.