Deep stall is a kind of stall affecting aircraft longitudinal dynamics in which the pitch up/down command is almost ineffective. The flight of the tail inside the separated wake of the stalled main wing could be considered as an explanation for the phenomenon. It implies a stable equilibrium at high angle of attack. The analysis is first performed from the observation that the different possible types of time evolutions in the (alpha, q) phase portrait are only in limited number. Then the damping of the short period mode near deep stall is noted to be smaller than the one at low angle-of-attack. At the end, the analysis of the dynamics proves to allow the identification of critical deep stall prone flight conditions without any a priori information on the aircraft.