Adaptive Replacement Cache (ARC) and CLOCK with Adaptive Replacement (CAR) are state-of-the- art "adaptive" cache replacement algorithms invented to improve on the shortcomings of classical cache replacement policies such as LRU, LFU and CLOCK. By separating out items that have been accessed only once and items that have been accessed more frequently, both ARC and CAR are able to control the harmful effect of single-access items flooding the cache and pushing out more frequently accessed items. Both ARC and CAR have been shown to outperform their classical and popular counterparts in practice. Both algorithms are complex, yet popular. Even though they can be treated as online algorithms with an "adaptive" twist, a theoretical proof of the competitiveness of ARC and CAR remained unsolved for over a decade. We show that the competitiveness ratio of CAR (and ARC) has a lower bound of N + 1 (where N is the size of the cache) and an upper bound of 18N (4N for ARC). If the size of cache offered to ARC or CAR is larger than the one provided to OPT, then we show improved competitiveness ratios. The important implication of the above results are that no "pathological" worst-case request sequences exist that could deteriorate the performance of ARC and CAR by more than a constant factor as compared to LRU.