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This paper investigates a non-autonomous slow-fast system, which isgeneralized by stochastic differential equations (SDEs) with locally Lipschitzcoefficients, subjected to standard Brownian motion (Bm) and fractionalBrownian motion (fBm) with Hurst parameter 1/2<H<1. We concentrate on how tohandle both types of integrals with respect to Bm and fBm and the locallyLispchitz continuity. The pathwise approach and the Ito stochastic calculus arecombined with the technique of stopping time to establish the averagingprinciple where the averaged equation is defined. Then, the slow component ofthe original slow-fast system converges to the solution of the proposedaveraged equation in the mean square sense is verified.

Stochastic averaging for the non-autonomous mixed stochastic differential equations with locally Lipschitz coefficients