This paper addresses the stability issue of delayed switched nonlinear systems whose subsystem is of the form (x) over dot(t) = A(t, x(t), x (t - d(t)))x(t) + B(t, x(t), x (t - d(t)))x (t - d(t)), that is, the system matrices depend on time and the present and past states. By means of a trajectory-based comparison approach, stability of original switched nonlinear system is transformed into that of a switched positive linear system called a comparison system. The involved delays are piecewise continuous and may be unbounded. The comparison switched system may consist of unstable subsystems. It is shown that if the comparison system is asymptotically or exponentially stable, then the original system is asymptotically or exponentially stable, globally or locally, depending on the domain chosen to form the comparison system. (C) 2018 The Authors. Published by Elsevier Ltd.