This paper surveys our researches on non-Newtonian viscosity effects, jump bifucation phenomena, and sudden unbalance response in squeeze-film dampers (SFD).The effects of a polymer thickened VI improved oil as pseudo-ptastastic fluid (PPF) on a SFD are investigated theoretically and experimentally. A modified Reynolds equation for pressure distribution of PPF in SFD has been derived and dynamic characteristics of SFD are evaluated. It is found that the film pressure distribution of PPF in SFD is smaller than that of a Newtonian fluid(NF), the centralized SFD is expected to have better film rigidity, while the uncen-tralized SFD is better in damping, the damping capacity of PPF film is inferior to that of NF film, and the effects of non-Newtonian viscosity on the dynamic characteristics of a SFD can be neglected in practice.The jump bifucation phenomena of a flexible rotor-SFD bearing system are examined with the aid of a Duffing equation. The phenomena that the frequency response curve of flexible rotor-SFD bearing system bends to right and becomes multivalued in a certain frequency range are due to the stiffening spring non-linearity of the squeeze-film force. The nonlinear cllaracteristics of the jump bifucation can, be estimated by the nature of the, backbone curves and boundary curves of the frequency response curve.A new mathematical model of sudden unbalance is introduced in calculating unbalance response. The analysis completed with this model shows that SFD is good at depressing the sudden unbalance vibration, and the uncentralized SFD is better than the centralized one in this aspect.