We provide a new methodology for smoothing in nonlinear state-space models with state-dependent variances. This general class of models contains both stochastic volatility (SVOL) and affine term structure models (ATSMs), which are widely used in financial time series. For our smoothing technique, we use simulation-based methods with an auxiliary mixture model. We illustrate our methodology with three applications. First, we show how to construct the auxiliary model for a simple exponential model. Second, we implement a stochastic volatility model with jumps for short-term interest rates in Hong Kong. We find strong evidence for jumps and stochastic volatility in the data, and provide the smoothing distribution for the jump times, sizes and variances. Third, we implement a two-factor affine term structure model for daily U.S. bond yields from 1996-1999. Our methodology uncovers the unobserved state vector and provides sharper estimates of the parameters of the state dynamics than a simple SVOL interest-rate model.