Summary: In survival analysis, accelerated failure time models are useful in modeling the relationship between failure times and the associated covariates, where covariate effects are assumed to appear in a linear form in the model. Such an assumption of covariate effects is, however, quite restrictive for many practical problems. To incorporate flexible nonlinear relationship between covariates and transformed failure times, we propose partially linear single index models to facilitate complex relationship between transformed failure times and covariates. We develop two inference methods which handle the unknown nonlinear function in the model from different perspectives. The first approach is weakly parametric which approximates the nonlinear function globally, whereas the second method is a semiparametric quasi-likelihood approach which focuses on picking up local features. We establish the asymptotic properties for the proposed methods. A real example is used to illustrate the usage of the proposed methods, and simulation studies are conducted to assess the performance of the proposed methods for a broad variety of situations.