Six acceptance conditions C₁—C₆ ofω-FA were known SO far．To look for some new acceptance condition of ω-FA and to study the power of ω-FA that accept ω-lan- guage with respect to the acceptance condition is one of hcart problem in theory of ω-finite state automata. This paper presents two types new acceptance condition Z₁ and Z₂ of ω-FA.The authors investigate(1)the power of ω-U-NFA that accept ω-language with re-spect to Z_i(i=1，2)and derive N^s_c3∈N^s_z2=N^s_z1=N^s_z1(2)the power ofω-NFA that ac．cept ω-language with respect to Z_i(i=1，2)and obtain N_c1∈N_z1∈N_z2．Some analogue results are dorrect with ω-DFA．