To calculate the depressurization and flow-coast-down accidents in a 1000-MW gas-cooled fast reactor (GCFR) with a secondary steam cycle, the PHAETON2 computer code is used, the emphasis being placed on the solution of one-dimensional unstationary helium flows. The fluid dynamics equations are solved one by one by a combination of implicit and explicit methods, taking into account most of the terms of the original equations. In the case of the accidents considered, the shutdown system is always activated, and inherent actions only of the GCFR are allowed. The results show a necessity of backup pressures above 150 kPa for the depressurization accidents and a minimum circulator frequency of 5 Hz for the flow-coastdown accidents.