This paper is devoted to construction and investigation of explicit forms of Wick tensor powers in general white noise spaces. We give an extension of some objects and structure of Gaussian analysis to the case of more general white noise measures on E * (the dual of a nuclear space E ), such that the random variable 〈 ω , ξ 〉 is infinitely divisible distributed for any ξ ∈ E and ω ∈ E * .