In this paper, we consider a pseudo-parabolic system with nonlinearities of variable exponent type (ut - Δut - div(|∇u|m(x)-2∇u) = |uv|p(x)-2uv² in Ω x (0, T), (vt - Δvt - div(|∇v|n(x)-2∇v) = |uv|p(x)-2u²v in Ω x (0, T), associated with initial and Dirichlet boundary conditions, where the variable exponents p(·), m(·), n(·) are continuous functions on
. We obtain an upper bound and a lower bound for blow-up time if variable exponents p(·), m(·), n(·) and the initial data satisfy some conditions. [ABSTRACT FROM AUTHOR]