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This paper is concerned with the Neumann initial-boundary value problem forthe two-species chemotaxis system with consumption of chemoattractant\begin{equation*}  u_t=\Delta u-\chi_1\nabla\cdot(u\nabla w), \end{equation*} \begin{equation*}  v_t=\Delta v-\chi_2\nabla\cdot(v\nabla w), \end{equation*} \begin{equation*}  w_t=\Delta w-(\alpha u+\beta v)w \end{equation*} in a smooth bounded domain$\Omega\subset\mathbb{R}^n$ ($n\geq2$), where the parameters $\chi_1$,$\chi_2$, $\alpha$ and $\beta$ are positive. It is proved that if\begin{equation*}\max\{\chi_1,\chi_2\}\|w(x,0)\|_{L^{\infty}(\Omega)}<\sqrt{\frac{2}{n}}\pi\end{equation*} the problem possesses a unique global classical solution thatis uniformly bounded. Moreover, we prove that \begin{equation*}u(x,t)\to\frac{1}{|\Omega|}\int_{\Omega}u(x,0),\quadv(x,t)\to\frac{1}{|\Omega|}\int_{\Omega}v(x,0)\quad\mbox{and}\quadw(x,t)\to0\quad\mbox{as}\ t\to\infty \end{equation*} uniformly with respect$x\in\Omega$.

Boundedness and stabilization in a two-species chemotaxis system with signal absorption