Clinical Natural Language Processing (NLP) systems extract clinical information from narrative clinical texts in many settings. Previous research mentions the challenges of handling abbreviations in clinical texts, but provides little insight into how well current NLP systems correctly recognize and interpret abbreviations. In this paper, we compared performance of three existing clinical NLP systems in handling abbreviations: MetaMap, MedLEE, and cTAKES. The evaluation used an expert-annotated gold standard set of clinical documents (derived from from 32 de-identified patient discharge summaries) containing 1,112 abbreviations. The existing NLP systems achieved suboptimal performance in abbreviation identification, with F-scores ranging from 0.165 to 0.601. MedLEE achieved the best F-score of 0.601 for all abbreviations and 0.705 for clinically relevant abbreviations. This study suggested that accurate identification of clinical abbreviations is a challenging task and that more advanced abbreviation recognition modules might improve existing clinical NLP systems.