Abstract.We provide equations for moduli spaces (of dimension <= 3) of semiquasihomogeneous singularities with fixed principal part, which we assume to be a Brieskorn-Pham polynomial. For dimension 4 and 5 we state only properties of the stabilizer and the invariant ring because the complexity of the calculation and/or the number of equations are too high. By these explicit computations we point out why a classification of more complicated singularities by means of unique normal forms fails due to the intrinsic complexity of moduli spaces.