This paper is concerned with a two-competing-species chemotaxis system involving singular sensitivity and indirect signal production ut=Δu-χ1∇·(uw∇w)+μ1u(1-u-a1v),(x,t)∈Ω×(0,∞),vt=Δv-χ2∇·(vw∇w)+μ2v(1-v-a2u),(x,t)∈Ω×(0,∞),τwt=Δw-w+z,(x,t)∈Ω×(0,∞),τzt=Δz-z+u+v,(x,t)∈Ω×(0,∞),\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} {\left\{ \begin{array}{ll}u_{t}=\Delta u-\chi _1\nabla \cdot (\frac{u}{w}\nabla w)+\mu _1 u(1-u-a_1v), &{}(x,t)\in \Omega \times (0,\infty ), \\ v_{t}=\Delta v-\chi _2\nabla \cdot (\frac{v}{w}\nabla w)+\mu _2 v(1-v-a_2 u), &{}(x,t)\in \Omega \times (0,\infty ),\\ \tau w_{t}=\Delta w -w+z,&{}(x,t)\in \Omega \times (0,\infty ),\\ \tau z_{t}=\Delta z-z+u+v,&{}(x,t)\in \Omega \times (0,\infty ),\\ \end{array}\right. } \end{aligned}$$\end{document}associated with homogeneous Neumann boundary conditions in a smooth bounded domain Ω⊂Rn\documentclass[12pt]{minimal}
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\begin{document}$$\Omega \subset R^{n}$$\end{document}, where the parameters χi,μi,ai(i=1,2)\documentclass[12pt]{minimal}
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\begin{document}$$\chi _{i},\mu _{i}, a_{i}(i=1, 2)$$\end{document} are assumed to be positive and τ∈{0,1}\documentclass[12pt]{minimal}
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\begin{document}$$\tau \in \{0,1\}$$\end{document}. By the method of some priori estimates and semigroup technique, when τ=1\documentclass[12pt]{minimal}
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\begin{document}$$\tau =1$$\end{document}, n≥2\documentclass[12pt]{minimal}
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\begin{document}$$n\ge 2$$\end{document}, it is proved that if max{χ1,χ2}<2n\documentclass[12pt]{minimal}
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\begin{document}$$\max \{\chi _{1}, \chi _{2}\}<\frac{2}{n}$$\end{document} the problem possesses a unique global classical solution. When τ=1\documentclass[12pt]{minimal}
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\begin{document}$$\tau =1$$\end{document}, n=2\documentclass[12pt]{minimal}
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\begin{document}$$n=2$$\end{document}, it can only require χi>0\documentclass[12pt]{minimal}
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\begin{document}$$\chi _{i}>0$$\end{document} for the existence of the global solution. In addition, when τ=0,n≥2\documentclass[12pt]{minimal}
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\begin{document}$$\tau =0, n\ge 2$$\end{document}, the global boundedness of the classical solution is determined as well.
