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When modelling financial data the jump-diffusion processes, driven by Wiener (W) and Poisson (N) processes, gain increasing importance. On the one hand, they explain better than the Itô diffusion the heavy tails of distributions of percentage changes of stock prices; on the other hand, unlike for example α-stable processes, they are based on the well developed mathematical tools for the Wiener and Poisson processes. After the identification of the jump times, e.g. by means of one of the so-called threshold methods, which are not linked with the continuous part of the model, the parameters from the continuous terms may be estimated similarly as for the Itô diffusion. But it is not obvious if the financial data after an extraction of jumps are already normally distributed. Therefore results of several normality tests will be presented here for chosen data from the Polish stock exchange market.