  This paper is concerned with the Neumann initial-boundary value problem for
the 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 that
is uniformly bounded. Moreover, we prove that \begin{equation*}
u(x,t)\to\frac{1}{|\Omega|}\int_{\Omega}u(x,0),\quad
v(x,t)\to\frac{1}{|\Omega|}\int_{\Omega}v(x,0)\quad\mbox{and}\quad
w(x,t)\to0\quad\mbox{as}\ t\to\infty \end{equation*} uniformly with respect
$x\in\Omega$.
