Stochastic partial differential equations (SPDEs) often have solutions that are known to be pure Schwartz distributions i.e. not functions. To make sense of such equations one needs to introduce some kind of smoothing parameters. This paper is concerned with stability properties of the solutions as one lets the smoothing parameters approach some kind of delta function. The first part of the paper concentrates on linear functionals in connection with SPDEs. In the second part we adress similar problems related to functionals of Hida distributions