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In this paper, we present recent work carried on μKlaim, a core calculus that retains most of the features of Klaim: explicit process distribution, remote operations, process mobility and asynchronous communication via distributed tuple spaces. Communication in μKlaim is based on a simple form of pattern matching that enables withdrawal from shared data spaces of matching tuples and binds the matched variables within the continuation process. Pattern matching is orthogonal to the underlying computational paradigm of μKlaim, but affects its expressive power. After presenting the basic pattern matching mechanism, inherited from Klaim, we discuss a number of variants that are easy to implement and test, by means of simple examples, the expressive power of the resulting variants of the language.