We are concerned with a class of n-dimensional non-autonomous delay differential equations obtained by adding a non-monotone delayed perturbation to a linear homogeneous cooperative system of delay differential equations. Sufficient conditions for the exponential asymptotic stability of the linear system are established. By using this stability, the permanence of the perturbed nonlinear system is studied. Under more restrictive constraints on the coefficients, the system has a cooperative type

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... ehaviour, in which case explicit uniform lower and upper bounds for the solutions are obtained. As an illustration, the asymptotic behaviour of a non-autonomous Nicholson system with distributed delays is analysed.