In this note, we discuss the problem of stability of (finite or infinite) families of continuous vector fields, all of them asymptotically stable but, in general, not exponentially stable. Under a multiple Liapunov function condition and an average dwell time constraint, we prove that the system possesses a form of stability, weaker than the standard one. The advantage of our results is that the conditions imposed on the Liapunov functions can be verified a priori, with no previous knowledge of the integral curves of the family.