Metal halide perovskite materials have been widely studied recently due to their excellent optoelectronic properties. Among these materials, organic-inorganic hybrid perovskites have attracted much attention because of their relatively soft framework, which makes them more suitable for nonlinear optical (NLO) applications. However, there is rare physical mechanism study on the coexistence of two-photon absorption (TPA) and saturable absorption (SA) in organic-inorganic hybrid perovskite materials. To clarify this issue, the NLO properties of mixed cation perovskite MA1-xFAxPbI3[MA=CH3NH3,FA=CH(NH2)2, x=0, 0.2, 0.4, 0.6, and 0.8] thin films are investigated in this paper. Based on the nonlinear transmittance and femtosecond-transient absorption spectrum measurements, it is found that the MA1-xFAxPbI3 materials exhibit NLO behavior dependent on excitation intensity. The TPA coefficient of MA1-xFAxPbI3 decreases with the increase of formamidinium (FA) content, while the relevant saturable intensity increases. In addition, it is revealed that the linear absorption process from valence band 2 to valance band 1 still exists even under a very low excitation intensity. With the increase of excitation intensity, the light transmittance at 1300 nm decreases first and then increases sharply, which also supports the explanation for the coexistence of TPA and SA. It is expected that our findings will promote the application of perovskite materials in nonlinear optoelectronic devices.