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This paper studies the average outage rate [or average level crossing rate (LCR)] and average outage duration (AOD) of wireless communication systems subject to cochannel interference. In particular, it presents closed-form expressions for the LCR and AOD when a minimum desired signal power requirement is specified for satisfactory reception. The results are quite general and account for systems operating over independent identically distributed Rician and/or Nakagami fading environments. When applicable, these new expressions are compared to those previously reported in the literature dealing with the LCR and AOD of 1) interference-limited systems when both the desired and interfering signals are subject to Rayleigh type of fading and 2) power-limited systems operating over Rician or Nakagami fading channels. Corresponding numerical examples that illustrate applications of the results are also provided and discussed. These results show that specifying a certain minimum desired signal power requirement induces a floor on the AOD. They also show that the AOD is essentially affected by the the maximum Doppler frequencies (or equivalently the speed) of the desired users.