In this work, we consider state-space models where the latent processes represent correlated mixtures of fractional Gaussian processes embedded in white Gaussian noises. The observed data are nonlinear functions of the latent states. The fractional Gaussian processes have interesting properties including long-memory, self-similarity and scale-invariance, and thus, are of interest for building models in finance and econometrics. We propose sequential Monte Carlo (SMC) methods for inference of the latent processes, where each method is based on different assumptions about the parameters of the state-space model. The methods are extensively evaluated via simulations of the popular stochastic volatility model.