This paper proposes a methodology for black-box identification and simulation of continuoustime nonlinear dynamical systems based on random process modeling and kriging. It is assumed that the (finite-dimensional) state vector is observed with noise at regularly or irregularly spaced instants. The proposed identification method consists of two steps. The first step is the estimation of the time derivatives of the state vector. The second step consists in the approximation of the controlled vector field. For the simulation of the system, a new integration scheme is proposed. This integration scheme makes it possible to deal consistently with the error of approximation of the vector field.