We discuss the formation of a common envelope system following dynamically unstable mass transfer in a close binary , and the subsequent dynamical evolution and final fate of the envelope . We base our discussion on new three-dimensional hydrodynamic calculations that we have performed for a close binary system containing a 4 M _ { \odot } red giant with a 0.7 M _ { \odot } main-sequence star companion . The initial parameters are chosen to model the formation of a system resembling V 471 Tau , a typical progenitor of a cataclysmic variable binary . The calculations are performed using the smoothed particle hydrodynamics ( SPH ) method with up to 5 \times 10 ^ { 4 } particles . As initial condition we use an exact hydrostatic equilibrium configuration at the onset of dynamically unstable mass transfer . The nonlinear development of the instability is followed using SPH until a quasi-static common envelope configuration is formed . In our highest-resolution calculation , we find evidence for a corotating region of gas around the central binary . This is in agreement with the theoretical model proposed by Meyer & Meyer-Hofmeister ( 1979 ) for the evolution of common envelope systems , in which this central corotating region is coupled to the envelope through viscous angular momentum transport only . We also find evidence that the envelope is convectively unstable , in which case the viscous dissipation time could be as short as \sim 100 dynamical times , leading to rapid ejection of the envelope . For V 471 Tau , our results , and the observed parameters of the system , are entirely consistent with rapid envelope ejection on a timescale \sim 1 yr and an efficiency parameter \alpha _ { CE } \simeq 1 .