Dynamical chaos, states stability in long Josephson junctions are investigated from the point of view of the flux quantization. It is shown that the stationary Meissner and fluxon states having integer number of fluxons are stable. Stationary antifluxon states also having integer number of the flux quanta and all other states with half-integer number of flux quenta are unstable. The transitions between all states - Meissner, the states having the integer and half-integer number of the flux quanta - take place in the nonstationary case, and all these states are dynamically equivalent, but the number of the flux quanta is a nonregular time-dependent functions for the chaotic states and regular for the regular ones.

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