To examine difficulties experienced by cochlear implant (CI) users when perceiving non-native speech, intelligibility of non-native speech was compared in conditions with single and multiple alternating talkers. Compared to listeners with normal hearing, no rapid talker-dependent adaptation was observed and performance was approximately 40% lower for CI users following increased exposure in both talker conditions. Results suggest that lower performance for CI users may stem from combined effects of limited spectral resolution, which diminishes perceptible differences across accents, and limited access to talker-specific acoustic features of speech, which reduces the ability to adapt to non-native speech in a talker-dependent manner.