For all 0 < q < +∞ the Privalov class Πq consists of all analytic functions f in a unit disk such that sup 0≤r<1 1/2π π −π ln + | f (re iθ)| q dθ < +∞. In this paper we solve a multiple interpolation problem in the class Πq for all 0 < q < 1. Namely, we find the sufficient conditions for the explicit construction of the function that solves the interpolation problem in the Privalov class. In addition, we discuss the necessity of these conditions.