Some investigations have been made on the evolution of the linear entropies of atom-field system, in which two identical two-level atoms simultaneously interact with a single-mode dissipative cavity field under large detuning. The effects of the initial atom states and the dissipative factors of the cavity on all linear entropies are also discussed. The results show that the influence of the cavity decay constant on different kinds of Bell states is completely different, and the state |Ψ〉12 is a robust entangled state against the decoherence while the state |Φ〉12 is a fragile entangled state.