Mixed effects models are popular tools for analyzing longitudinal data from several individuals simultaneously. Individuals are described by N independent stochastic processes (Xi(t), t ∈ [0, T ]), i = 1,. .. , N , defined by a stochastic differential equation with random effects. We assume that the drift term depends linearly on a random vector Φi and the diffusion coefficient depends on another linear random effect Ψi. For the random effects, we consider a joint parametric distribution leading to explicit approximate likelihood functions for discrete observations of the processes Xi on a fixed time interval. The asymptotic behaviour of the associated estimators is studied when both the number of individuals and the number of observations per individual tend to infinity. The estimation methods are investigated on simulated and real neuronal data.