Abstract: In this paper the general definitions of the strong Markov property and the strong optional （predicable, accessible, torally inaccessible） Markov property for twoparamoter processes are proposed and the relations between various strong Markov properties are discussed. These results are similar to those for one-parameter processes in 1. Moreover, the following result is shown: two-parameter Feller processes with right continuous sample funotions possess the strong optional Markov property.