In this work, for a reference filtration F, we develop a method for computing the semimartingale decomposition of F-martingales in a specific type of en-
largement of F. As an application, we study the progressive enlargement of F with a sequence of non-ordered default times and show how to deduce results concerning the first-to-default, kth-to-default, k-out-of-n-to-default or all-to-default events. In particular, using this method, we compute explicitly the semimartingale decomposition of F-martingales under the absolute continuity condition of Jacod.

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