In continuous time, rates of convergence for nonparametric density estimators are related with sample paths regularity of the underlying process. In this paper, we propose and study two families of estimators for the local Hlder exponent, γ, of multivariate continuous time processes. For observed sample paths over [0, T_n], T_n ↑ ∞, we use increment-based type estimators and give their almost sure rates of convergence for strongly mixing processes. It is shown that these rates may depend on an extra parameter, β, corresponding to second order regularity of the observed process. To avoid such a difficulty, a family of preliminary estimators of β is also given and studied.