<p>Significant progress has been achieved in the study of switched homogeneous systems with degree greater than one. Nevertheless, the investigation of systems with degree less than one, especially those characterized by time-varying dynamics, encounters substantial challenges. This paper concentrates on investigating the stability issue of time-varying switched homogeneous systems (TVSHSs) with degree less than one. First, we establish an exponential stability criterion via the comparison principle and a non-Lyapunov functional method specifically developed for positive systems, deriving sufficient conditions under average dwell time (ADT) switching strategies. Then, a finite-time stability criterion is derived for delay-free systems with degree strictly less than one, providing explicit estimates of the settling time for system states. The stability conditions presented in this paper are more general and intuitive than those in existing studies and remain applicable to systems with unbounded parameters. In conclusion, simulation examples are provided to demonstrate the feasibility of the proposed stability conditions.</p>