This paper deals with stochastic weight update methods for neural networks learning. We will study two methods, stochastic weights selection and stochastic neurons selection. These methods have to allow better parallelization of the backpropagation algorithm, although in this paper we will use only the conventional serial implementation. We will use meteorological data for experimentation with neural networks based weather prediction. We will show that proposed methods can be used to replace regular backpropagation, but in the serial implementation they are not efficient.