The main aims of the NA61/SHINE experiment are to discover the critical point of strongly interaction matter and to study the properties of the onset of deconfinement. For this goal the scan through two dimensional phase diagram (T-mu_B) is being performed at the SPS by measurements of hadron production in proton-proton, proton-nucleus and nucleus-nucleus interactions as a function of collision energy and system size. It is supposed that fluctuations of different dynamical quantities will increase close to the critical point and this effect could be observed in this 2D scan. In this report we present the recent results of measurements of fluctuations in p+p and Be+Be collisions at SPS energies. Comparison with the model predictions and the corresponding data of other experiments will be shown and discussed.