Based on analysis of photometric observations of nearby M type stars obtained with ASAS, 31 periodic variables were detected. The determined periods are assumed to be related to rotation periods of the investigated stars. Among them 10 new variables
with periods longer than 10 days were found, which brings the total number of slowly rotating M stars with known rotation periods to 12 objects. X-ray activity and rotation evolution of M stars follows the trends observed in G-K type stars. Rapidly rotating stars are very active and activity decreases with increasing rotation period but the period-activity relation is mass-dependent which suggests that the rotation period alone is not a proper measure of activity. The investigated stars were grouped according to their mass and the empirical turnover time was determined for each group. It increases with decreasing mass more steeply than for K type stars for which a flat dependence had been found. The resulting Rossby number-activity relation shows an exponential decrease of activity with increasing Rossby number. The analysis of space motions of 27 single stars showed that all rapidly rotating and a few slowly rotating stars belong to young disk (YD) whereas all old disk (OD) stars are slowly rotating. The median rotation period of YD stars is about 2 days and that of OD stars is equal to 47 days, i.e. nearly 25 times longer. The average X-ray flux of OD stars is about 1.7 dex lower than YD stars in a good agreement with the derived Rossby number-activity formula supplemented with rotation-age relation and in a fair agreement with recent observations but in a disagreement with the Skumanich formula supplemented with the activity-rotation relation.
