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Recent studies have shown that asynchronous non- orthogonal multiple access (ANOMA) outperforms conventional synchronous non-orthogonal multiple access (NOMA) by taking advantage of artificial timing mismatch with oversampling. For the first time, we comprehensively study the impact of timing errors on the performance of uplink ANOMA systems in this paper. We consider two types of timing errors, which are the synchronization timing error and the coordination timing error. We analyze how the timing errors affect ANOMA systems, and derive the throughput loss of ANOMA systems incurred by both the synchronization timing error and the coordination timing error. An interesting finding is that the synchronization timing error has a larger impact on the throughput performance of ANOMA systems compared with the coordination timing error.