The quasilinear differential systemx' = ax + b vertical bar y vertical bar(p)*(-2)y + k(t, x, y), y' = c vertical bar x vertical bar(p-2)x + dy + l(t, x, y)is considered, where a, b, c and dare real constants with b(2) + c(2) > 0, p and p* are positive numbers with (1/p) + (1/p*) = 1, and k and l are continuous for t >= t(0) and small x(2) + y(2). When p = 2, this system is reduced to the linear perturbed system. It is shown that the behavior of solutions near the origin (0, 0) is very similar to the behavior of solutions to the unperturbed system, that is, the system with k equivalent to l equivalent to 0, near (0, 0), provided k and l are small in some sense. It is emphasized that this system can not be linearized at (0, 0) when p not equal 2, because the Jacobian matrix can not be defined at (0, 0). Our result will be applicable to study radial solutions of the quasilinear elliptic equation with the differential operator r(-(gamma-1))(r(alpha)vertical bar u'vertical bar(beta-a)u')', which includes p-Laplacian and k-Hessian. (C) 2020 The Authors. Published by Elsevier Inc.