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We describe the extension to multiple datasets of a coherent method for thesearch of continuous gravitational wave signals, based on the computation of5-vectors. In particular, we show how to coherently combine different datasetsbelonging to the same detector or to different detectors. In the latter casethe coherent combination is the way to have the maximum increase insignal-to-noise ratio. If the datasets belong to the same detector theadvantage comes mainly from the properties of a quantity called {\it coherence}which is helpful (in both cases, in fact) in rejecting false candidates. Themethod has been tested searching for simulated signals injected in Gaussiannoise and the results of the simulations are discussed.

Coherent search of continuous gravitational wave signals: extension of the 5-vectors method to a network of detectors