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This technical note addresses the stability problem of delayed positive switched linear systems whose subsystems are all positive. Both discrete-time systems and continuous-time systems are studied. In our analysis, the delays in systems can be unbounded. Under certain conditions, several stability results are established by constructing a sequence of functions that are positive, monotonically decreasing, and convergent to zero as time tends to infinity (additionally continuous for continuous-time systems). It turns out that these functions can serve as an upper bound of the systems' trajectories starting from a particular region. Finally, a numerical example is presented to illustrate the obtained results.