The current-voltage (I-V) characteristics of two parallel connected MgB2 microbriges (with width of 3 μm and the diameter of the quantization loop of about 3 μm) have been measured at varius temperatures in the constant current regime. This circuit was made by a laser scribing (nitrogen laser with wavelength of 337 nm) from a textured a-axis oriented MgB2 film grown on MgO (100) substrates (see fig. 1) with the critical temperature of 37,7 K. The critical temperature of the prepared microbrige was lower than Tc of the film because of the sample inhomogeneity. It was found from an X-ray diffraction analysis that the coherent scattering region (the size of crystallites) calculated on the basis of the halfwidth of the (100) MgB2 diffraction peak is about 45 – 50 nm. All the I-V characteristics were registered during the current sweeping from -Imax to + Imax and back (fig. 2). As we can see from the fig. 2, the I-V curves are hysteretic and have the voltage steps and an excess current. The voltage steps on the curves can be explained either by formation of phase slip centers or lines [1] or by switching of a network of Josephson junctions to the resistive state [2]. For phase slip phenomenon is typical a presence of an excess current and a constant differential resistance of steps. In our case, however, the main feature of the voltage steps is nonlinearity, i.e. the differential resistance slightly decreases with increasing current. This nonlinearity can, probably, be related to resistivity of the flux motion. On the fig. 3 the temperature dependence of the critical current is presented. In order to determine which mechanism of resistivity works it is necessary to study Josephson properties of microbridges [3] and to conduct low temperature laser microscopy scanning [4] for a visualization of the spatial distribution of resistive areas along microbridges. The proposed experiments are in progress. The temperature dependence of the critical current measured for this structure is different from that for “classical” superconductors, perhaps, due to two band superconductivity of MgB2 (fig. 3), namely below a certain temperature we can see a certain ambiguity of the critical currentfigureFigure 1. X-ray diffraction pattern of a MgB2 film grown on MgO (100) substrate.figureFigure 2. The I-V characteristics of two parallel connected MgB2 microbriges at different temperaturesfigureFigure 3. The temperature dependence of the critical current measured for this structure