Abstract: A cusp catastrophe model of landslides was presented and the necessary and sufficient conditions leading to landslides were discussed.The sliding surface of the landslides was assumed to be planar and was a combination of two media: medium 1 was elasto-brittle or strain-hardening and medium 2 was strain-softening.The shear stress-strain constitutive model for the strain-softening medium was described by the Weibull’s distribution law.It was found that the instability of the slope relied mainly on both the stiffness ratio and the homogeneity index of the media and that a new role of water was to enlarge the material homogeneity or brittleness and hence to reduce the stiffness ratio.A nonlinear dynamical model(or called a physical forecasting model),which was derived by considering the time-dependent behavior of the strain-softening medium,was used to study the time prediction of landslides.An algorithm of inversion on the nonlinear dynamical model was suggested for seeking the precursory abnormality and abstracting mechanical parameters from a series of observed landslide.A case study of the Jimingsi landslide was conducted and its nonlinear dynamical model was established from the observation series using the algorithm of inversion.It was found that the catastrophic characteristic index |D| closed to zero prior to instability after it attained a high peak value and the slope evolved into the tertiary creep,and it could be regarded as an important precursory abnormality index.By taking into account the evolutionary characteristic of the slope in the secondary creep,a simplified nonlinear dynamical model was put forward for studying the properties of bifurcation and chaos.It was revealed that the emergence of chaos depended on the mechanical parameters of the sliding-surface media.