Abstract: Let E be a countable set, Z_+=\0,1,2, \cdots\ and Z_+^2=\left\(n, m): n, m \in Z_+\right\. We denote (n, m) \geqslant(u, v) if (n, m),(u, v) \in Z_+^2 and n \geqslant u, m \geqslant v. Let X be the set of all functions \gamma_l(\cdot, \cdot) on Z_+^2 with values in E. This is the canonical path space for a two parameter Markov process with state space E. Let \mathscrA be the smallest \sigma-algebra on X relative to which all mappings \eta(\cdot, \cdot) are measurable. For (u, v) \in Z_+^2, let \mathscrF_u v^*=\sigma(\eta(s, t):(s, t) \in Z_+^\stackrel2+, s \leqslant u or t \leqslant v ). Let \mathscrP denote the set of all probability measures on (X, \mathscrA). Delinition: Suppose P \in \mathscrP.\left\\eta(n, m),(n, m) \in Z_+^2\right\ is said to be a two parameter Markov process on (X, \mathscrA, P), if for any \doti \in E and (n, m) \geqslant(u, v), P\left(\eta_l(n, m)=i \mid \mathscrF_u c^*\right)=P(\eta(n, m)=i \mid \eta(u, v), \eta(u, m), \eta(n, v)) . Let Z=\\cdots,-1,0,1, \cdots\ and Z_n=\left\(u, v):(u, v) \in Z_+^2, u \wedge v=n\right\, n \in Z_+. We define the mapping \varphi_n from Z_n onto Z : \varphi_n(u, v)=u-v, \quad(u, v) \in Z_n and the mapping \psi_n form E^Z_n onto E^z : \tilde\eta_n(u-v)=\psi_n(\eta)(u-v)=\eta(u, v), \quad \eta \in E^Z_n,(u, v) \in Z_n . Let E^Z be the set of all functions \tilde\eta(\cdot) on Z with values in E and \mathscrB be the smallest \sigma algebra on E^Z relative to which all mappings \tilde\eta(\cdot) are measurable. For any n_1, \cdots, n_k \in Z_+, G_1, \cdots, G_k \in \mathscrB, let \beginaligned & \widetildeP\left(\left(\tilde\eta_0, \tilde\eta_1, \cdots\right) \in\left(E^Z\right)^Z_t: \tilde\eta_n_1 \in G_1, \cdots, \tilde\eta_n_k \in G_k\right) \\ & \quad=P\left(\left(\eta_0, \eta_1, \cdots\right) \in X: \eta_n_1 \in \psi_n_1^-1\left(G_1\right), \cdots, \eta_n_k \in \psi_n_k^-1\left(G_k\right)\right) \endaligned then \widetildeP is a probabilty measure on \left(\left(E^z\right)^z, \mathscrB^Z_+\right). Theorem: Suppose that \left\\eta(n, m),(n, m) \in Z_+^2\right\ is a two parameter Markov process on ( X, \mathscrA, P ) with state space E, then \left\\tilde\eta_n, n \in Z_+\right\is a one parameter Markov process on \left(\left(E^Z\right)^Z_+, \mathscrB^Z_+, \widetildeP\right) with state space E^Z.