In this paper, by using the so-called dynamical approach we study the existence of nontrivial solutions for a class of Kirchhoff type systems. The presented result is a generalization of previous works Alves and Boudjeriou (Nonlinear Anal. 197:1–17, 2020; Rend. Circ. Mat. Palermo 71(2):611–632, 2022) where the existence of nontrivial solutions for some scalar nonlocal elliptic problems has been studied.