Abstract: In this paper the necessary and sufficient ocndition in terms of *-transition functions is given for a two-parameter process to be a regular *-Markov process.The existence of regular *-Markov processes is proved.It is shown that a two-parameter process has independent increments（resp.stationary independent increments）if and only if it is a spatially homogeneous（resp.homogeneous and spatially homogeneous） *-Markov process.