In a conventional mobile environment, mobile clients retrieve data items from database servers via mobile support stations, by downloading the items over scalable broadcast channels (push-based), requesting them over shared point-to-point channels (pull-based), or making use of both types of channels to retrieve them (hybrid). Caching is a key technique for improving data retrieval performance of mobile clients, regardless of the data delivery mechanism. The emergence of robust peer-to-peer technologies now brings to reality what we call "cooperative caching" in which mobile clients can access data items from the cache in their neighboring peers, thereby adding a new dimension for data caching. This paper studies the system performance of a cooperative caching scheme, called COCA, in a hybrid data delivery environment, and proposes a cooperative cache replacement scheme, called CORE, for mobile systems. The performance of COCA and CORE schemes is evaluated through a number of simulated experiments. The experiment results show that COCA effectively improves the system performance in push-based and hybrid data delivery environments, especially in a heavily-loaded environment. The results also indicate that CORE can further improve on the access latency and reduce the number of expensive server requests, which consume scarce pull-based bandwidth.