The author considers models of the formcontaining as special cases the finite dimensional regression models. Let β(μ) be an unknown functionfor u ∈U⊆R1andx(s, u)be known functions being integrable relative tou.Let further be. Knowing a realisation of the processyt,t∈Tthe processys,s∈Sshall ne predicated. As risque of a predictionp(s)ofyswe utilizeUnder certain propositions the author determines a best linear homogeneous resp, a best linear homogeneous unbiased resp a best linear inhomogeneous prediction using functional analytical methods without demanding regularity properties of the covariance operator from ϵt.