The validity of the traditional local diffusive approach and of the use of monoenergetic calculations has been studied for the stellarator TJ-II (Alejaldre et al., 1990): it is shown to be doubtful, under some circumstances, even in a purely collisional description of transport. The diffusion in physical space starting from Dirac-delta-like initial conditions has been studied using the code Integrator of Stochastic Differential Equations for Plasmas by Castejón et al. (2007). Particles may experience large radial excursions from their original magnetic surfaces in a single collisional time. The contribution of these particles to the flux may make it nondiffusive; non-Gaussian density distributions, characterized by long tails, are observed. In the velocity space, there are important variations in the average particle kinetic energy after one collision time. We discuss the effect of this fact over the calculation of monoenergetic transport coefficients and their convolution. A simple analysis based on Hurst exponents has shown nevertheless that the description of transport by means of a pinch term and an effective transport coefficient is more correct than expected.