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The thesis concentrates on property of linearity in time series models, its definitions and possibilities of testing. Presented tests focus mainly on the time domain; these are based on various statistical methods such as regression, neural networks and random fields. Their implementation in R software is described. Advantages and disadvantages for tests, which are implemented in more than one package, are discussed. Second topic of the thesis is additivity in nonlinear models. The definition is introduced as well as tests developed for testing its presence. Several test (both linearity and additivity) have been implemented in R for purposes of simulations. The last chapter deals with application of tests to real data.