Here we demonstrate how the study of Gaussian stochastic processes is possible by comparing their covariance functions. For this purpose, we need some preordering relations in the class Φ+(T) of real-valued positive functions given on a set T of parameters. As a rule, T will be a separable metric space. In particular, the following situations are of especial interest to us: T = {1, 2,…, m} where m ≥ 1 is a natural number; T = N; T = [0,1]; T = R or T = R + = {t ∈ R : t ≥ 0}.