Abstract: Int S be a countable set and E=\left(Z^d\right)^s the configuration space, \left(P_i(u, v): u, v \in S\right) is a Markov matrix representing diffusion kernel of i-species. (q_u(k, j): k, j \in Z ) is a Q matrix representing reactions among the species in position u \in S. In the paper, we use two kinds of distance. One is \rho(\eta, \xi)-\sum_u \in \mathcalS(1-\delta(\eta(u), \xi(u))) \alpha(u) \quad \eta, \xi \in E where a is a strict positive function on S, it is summable and satisfies \sum_v \in B\left(\sum_v=1^d P_i(u, v)\right) \alpha(v) \leqslant M \alpha(u) \quad u \in S. On the other hand, the norm of \eta \in E induces a distance on \mathscrE-(\eta \in E:\|\eta\|< \infty), which we call norm distance. The set of all Lipschitz function on E, relative to \rho, is denoted by \mathscrL^\prime \prime and the one on \mathscrE, relative to the norm distanoe, is denoted by \mathscrL. The formal generator of a multi-species reaction-diffusion processes(M. R. D. P) is that \beginaligned \Omega f(\eta)= & \sum_w \in s \sum_k=0 q_u(\eta(u), \eta(u)+k)(f(\eta+k e)-f(\eta)) \\ & +\sum_\mathbfv \in \mathbbB \sum_i=1^n O_w i(\eta(u)) \sum_v \neq \mathrmv P_\mathbfv(u, v)\left(f\left(\eta-e_\mathrmw+e_\mathrmkq\right)-f(\eta)\right) \quad f \in \mathscrL^\circ, \eta \in H \endaligned where e_\mathrmwt is a unit vector in E, k e_\mathrmu=\sum_i=1^n k_i e_\mathrmwi. \quad H is a \sigma-ompact subset of E. If 0 \leqslant C_\mathrmus(\eta(u)) \leqslant R \quad \text and \quad C_\mathrmu(0)=0 \text , and the following condition holds: there exists a nonnogative, non-deoreasing function B on Z_+^d such that (1) B(k) \rightarrow \infty as |k| \rightarrow \infty (2) q_\mathbfu(j) \equiv \sum_k+1 q_\mathbfv(j, j+k) \leqslant B(j) (3) B\left(\eta(u)+e_w(u)\right)-B(\eta(u)) \leqslant c B(\eta(u))+d \quad i=1,2, \cdots, d (4) \sum_k=0 q_u(\eta(u), \eta(u)+k)(B(\eta(u)+k)-B(\eta(u))) \leqslant a B(\eta(u))+b where, a, b, c, d are nonnegative constants, then there exists a unique constraet semigroup S(t) on \mathscrL^\circ with the generator \Omega, and there exists a Markov process ( \left.\left(\eta_t\right), p^\eta\right), associated with \boldsymbolS(t). Moreover, if \sum_k=0\left(q_u(\eta(u), \eta(u)+k) \sum_i=1^n k_i\right) \leqslant a_1 \sum_i=1^n \eta_i(u)+b_1, then P(t, \eta, \mathscrE)=1 for any \eta \in \mathscrE. Therefore, the state space of M. R. D. P can be restricted to \mathscrE and the domain of S(t) can be extended to \mathscrL.