  This paper deals with the quasilinear attraction-repulsion chemotaxis system
\begin{align*}
  \begin{cases}
  u_t=\nabla\cdot \big((u+1)^{m-1}\nabla u
  -\chi u(u+1)^{p-2}\nabla v
  +\xi u(u+1)^{q-2}\nabla w\big),\\[]
  0=\Delta v+\alpha u-\beta v,\\[]
  0=\Delta w+\gamma u-\delta w
  \end{cases} \end{align*} in a bounded domain $\Omega \subset \mathbb{R}^n$
$(n \in \mathbb{N})$ with smooth boundary $\partial \Omega$, where $m, p, q \in
\mathbb{R}$, $\chi, \xi, \alpha, \beta, \gamma, \delta>0$ are constants. In the
case that $m=1$ and $p=q=2$, when $\chi\alpha-\xi\gamma<0$ and $\beta=\delta$,
Tao-Wang (Math. Models Methods Appl. Sci.; 2013; 23; 1-36) proved that global
bounded classical solutions toward the spatially constant equilibrium
$(\overline{u_0}, \frac{\alpha}{\beta}\overline{u_0},
\frac{\gamma}{\delta}\overline{u_0})$ via the reduction to the Keller-Segel
system by using the transformation $z:=\chi v-\xi w$, where $\overline{u_0}$ is
the spatial average of the initial data $u_0$. However, since the above system
involves nonlinearities, the method is no longer valid. The purpose of this
paper is to establish that global bounded classical solutions converge to the
spatially constant equilibrium $(\overline{u_0},
\frac{\alpha}{\beta}\overline{u_0}, \frac{\gamma}{\delta}\overline{u_0})$.
