This note investigates the stability of both linear and nonlinear switched systems with average dwell time. Two new analysis methods are proposed. Different from existing approaches, the proposed methods take into account the sequence in which the subsystems are switched. Depending on the predecessor or successor subsystems to be considered, sequence-based average preceding dwell time (SBAPDT) and sequence-based average subsequence dwell time (SBASDT) approaches are proposed and discussed for both continuous and discrete time systems. These proposed methods, when considering the switch sequence, have the potential to further reduce the conservativeness of the existing approaches. A comparative numerical example is also given to demonstrate the advantages of the proposed approaches.