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This paper deals with the boundedness of solutions to the following quasilinear chemotaxis-haptotaxis model of parabolic-parabolic-ODE type: ⎧ ⎪ ⎨ ⎪ ⎩ u t = ∇ • (D(u)∇u)-χ ∇ • (u∇v)-ξ ∇ • (u∇w) + μu(1-u r-1-w), x ∈ Ω, t > 0, v t = v-v + u η , x ∈ Ω, t > 0, w t =-vw, x ∈ Ω, t > 0, under zero-flux boundary conditions in a smooth bounded domain Ω ⊂ R n (n ≥ 2), with parameters r ≥ 2, η ∈ (0, 1] and the parameters χ > 0, ξ > 0, μ > 0. The diffusivity D(u) is assumed to satisfy D(u) ≥ δu-α , D(0) > 0 for all u > 0 with some α ∈ R and δ > 0. It is proved that if α < n+2-2nη 2+n , then, for sufficiently smooth initial data (u 0 , v 0 , w 0), the corresponding initial-boundary problem possesses a unique global-in-time classical solution which is uniformly bounded.

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