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 $$ \rho(\eta, \xi)-\sum_{u \in \mathcal{S}}(1-\delta(\eta(u), \xi(u))) \alpha(u) \quad \eta, \xi \in E $$ 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 $ \mathscr{E}-(\eta \in E:\|\eta\|< \infty)$, which we call norm distance. The set of all Lipschitz function on $E$, relative to $\rho$, is denoted by $ \mathscr{L}^{\prime \prime}$ and the one on $\mathscr{E}$, relative to the norm distanoe, is denoted by $ \mathscr{L}$. The formal generator of a multi-species reaction-diffusion processes(M. R. D. P) is that $$ \begin{aligned} \Omega f(\eta)= & \sum_{w \in s} \sum_{k=0} q_u(\eta(u), \eta(u)+k)(f(\eta+k e)-f(\eta)) \\ & +\sum_{\mathbf{v} \in \mathbb{B}} \sum_{i=1}^n O_{w i}(\eta(u)) \sum_{v \neq \mathrm{v}} P_{\mathbf{v}}(u, v)\left(f\left(\eta-e_{\mathrm{w}}+e_{\mathrm{kq}}\right)-f(\eta)\right) \quad f \in \mathscr{L}^{\circ}, \eta \in H \end{aligned} $$ where $e_{\mathrm{wt}}$ is a unit vector in $E, k e_{\mathrm{u}}=\sum_{i=1}^n k_i e_{\mathrm{wi}}. \quad H$ is a $\sigma$-ompact subset of $E$. If $$ 0 \leqslant C_{\mathrm{us}}(\eta(u)) \leqslant R \quad \text { and } \quad C_{\mathrm{u}}(0)=0 \text {, } $$ 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) $q_{\mathbf{u}}(j) \equiv \sum_{k+1} q_{\mathbf{v}}(j, j+k) \leqslant B(j)$ (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 $\mathscr{L}^{\circ}$ with the generator $\Omega$, and there exists a Markov process ( $\left.\left(\eta_t\right), p^\eta\right)$, associated with $\boldsymbol{S}(t)$. 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 $P(t, \eta, \mathscr{E})=1$ for any $\eta \in \mathscr{E}$. Therefore, the state space of M. R. D. P can be restricted to $\mathscr{E}$ and the domain of $S(t)$ can be extended to $\mathscr{L}$.