We deal with real weakly stationary processes \procX with non-positive autocorrelations {rk}, i. e. it is assumed that rk≤0 for all k=1,2,…. We show that such processes have some special interesting properties. In particular, it is shown that each such a process can be represented as a linear process. Sufficient conditions under which the resulting process satisfies rk≤0 for all k=1,2,… are provided as well.