[en] The tangent algorithm for event (nuclear interaction) searching by signals detected at the output of the Mesooptical Fourier-Transform Microscope (MFTM) in the vicinity of the focal circle is given. It is shown that the signals at the output of the MFTM used in this algorithm are lying on the straight line of particle tracks form the event. An example if realization of the tangent algorithm for event searching in the case of a fourtrack event is considered. A description is given of the algorthm for direct observation of the events in the nuclear research emulsion which requires neither the detection of the signals at the MFTM output for single particle tracks, nor their subsequent processing. It is shown that the MFTM runs for two given algorithm for event searching 10³ times faster than for the manual searching