Relativistic stochastic processes in μ-space are defined and studied in a completely (and manifestly) covariant manner, without particularizing the time variable. It is shown that a number of usual definitions such as ``Gaussian process,'' etc., cannot be given a fully invariant meaning. Markovian processes are also studied. We find anew, as a particular case, results already obtained by Łopuszaǹski [Acta Phys., Polon. 12, 87 (1953)] in the case of Markovian processes in Minkowski space-time. Several suggestions are made to generalize these results.