One form of developmental difficulty with arithmetic affects the storage or retrieval of arithmetical facts, such as tables, which are required to implement arithmetical computations (Temple, 1991, 1994). Such difficulties may arise because of impairment in a specialized system for the storage of arithmetical facts or as a result of causally linked impairment in another cognitive domain. This study explored issues concerning the representation and retrieval of arithmetical facts in children with number fact disorders (NF) and in normal children, in particular the status of hypothesized linked impairments: short-term memory (STM) spans, counting skills, speed of speech, and speed of number fact and lexical retrieval. There was no evidence that NF children had weak STM spans on any span measure or that STM spans related to arithmetical fact skills. There was also no evidence that NF children had weak counting abilities or free counting speeds. The NF children were slower in speeded counting, which also correlated with number fact skill. The significance or not of this is discussed. The NF children were also slower than controls in speed of speech and on some measures of speed of access. However, the absence of correlation with number fact skill, the absence of generality across tasks, and the possibility that delayed speeds in fact retrieval reflect the use of alternative strategies, together suggest that the increased speeds are not causally linked to number fact skill. The results are consistent with modular accounts, in which there is a specialized system for the storage and retrieval of arithmetical facts.