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The formulation of a comprehensive theory of the glassy state and of the glass transition remains one of the challenges for modern physics [1]. This is one of the reasons of the continuing interest in analysis of these problems. In addition, also from a practical viewpoint, experimental study and theoretical description of glass transition are very important topics, due to the wide distribution of modern technological applications of glasses as well as their frequent occurrences in everyday life. Polymers are known to be good glass formers, allowing one to study glass transition effects as well as to verify the applicability of various theoretical models [2]. In the presented work experimental and theoretical investigations of glass transition of atactic polystyrene (PS) in a broad range of cooling rates (5•10-6-2 K/s) were performed [3]. The capability of commonly employed theoretical techniques for Cp modeling to describe the obtained data is considered. It is shown that the extended Tool-Narayanaswamy-Moynihan (TNM) model with Vogel-Fulcher-Tammann-Hesse (VFTH) or Adam-Gibbs (AG) expressions for relaxation time with the common single set of parameters do not fit the experimental data well. Moreover, the values of parameters required to produce an adequate fit of the whole set of heating curves are quite different from their estimates obtained from independent additional experiments. An additional expression for relaxation time is proposed within the Gutzow-Schmelzer (GS) approach for describing the kinetics of glass transition leading to results of similar precision. The obtained results reconfirm the general conclusion that the considered models of glass transition require parameter readjusting for different cooling or heating rates in order to adequately describe the experimental data. The first results of neutron reflectivity measurements of glass transition of PS thin films on the silicon substrate, performed at the GRAINS spectrometer of the IBR-2M reactor, JINR are briefly reported. The perspectives of neutron measurements at these setup are discussed.