In many applications Gaussian processes serve as models for random influences. Especially in reliability problems, they ae used for describing the state of technical systems. In technical applications it is assumed in general that the processes are differentiable. In the following we will consider a stationary, ergodic Gaussian vector process \b{X}(t)\(=(X_ 1(t),...,X_ n(t))\) of n independent, identically distributed stationary Gaussian processes \(X_ i(t)\) with \(E(X_ i(t))=0\) and \(Var(X_ i(t))=1\). Further we shall assume that each sample path \(X_ i(t)\) is twice continuously differentiable with probability 1.