Results of the time variability monitoring of the two classical T Tauri stars, RU Lup and IM Lup, are presented. Three photometric data sets were utilised: (1) simultaneous (same field) MOST satellite observations over four weeks in each of the years 2012 and 2013, (2) multicolour observations at the SAAO in April - May of 2013, (3) archival V-filter ASAS data for nine seasons, 2001 - 2009. They were augmented by an analysis of high-resolution, public-domain VLT-UT2 UVES spectra from the years 2000 to 2012. From the MOST observations, we infer that irregular light variations of RU Lup are caused by stochastic variability of hot spots induced by unstable accretion. In contrast, the MOST light curves of IM Lup are fairly regular and modulated with a period of about 7.19 - 7.58 d, which is in accord with ASAS observations showing a well defined 7.247+/-0.026 d periodicity. We propose that this is the rotational period of IM Lup and is due to the changing visibility of two antipodal hot spots created near the stellar magnetic poles during the stable process of accretion. Re-analysis of RU Lup high-resolution spectra with the Broadening Function approach reveals signs of a large polar cold spot, which is fairly stable over 13 years. As the star rotates, the spot-induced depression of intensity in the Broadening Function profiles changes cyclically with period 3.71058 d, which was previously found by the spectral cross-correlation method.
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