We present the results of a five-day monitoring campaign with XMM-Newton of six X-ray bright young stellar objects (YSOs) in the star-forming complex L1551 in Taurus. All stars present significant variability on the five-day time scale. Modulation of the light curve on time scales comparable with the stars rotational period appeared to be present in the case of one weak-lined T Tauri star. Significant spectral variations between the 2000 and the 2004 observations were detected in the (unresolved) classical T Tauri binary system XZ Tau: a hot plasma component which was present in the X-ray spectrum in 2000 had significantly weakened in 2004. As XZ Tau N was undergoing a strong optical outburst in 2000, which had terminated since then, we speculate on the possible relationship between episodic, burst accretion, and X-ray heating. The transition object HL Tau underwent a strong flare with a complex temperature evolution, which is indicative of an event confined within a very large magnetic structure (few stellar radii), similar to the ones found in YSOs in the Orion Nebula Cluster.