The results presented in this work refer to the investigation of the mechanics of the interaction between two important systems of nuclear power plants, i.e.: the Primary (PS) and Secondary (SS) systems. The influence of these effects on the response spectra is studied, in convenient points of the structure where could exist pipeline (SS) supports. Two different approaches are used to generate the response spectra: the first neglects the interaction between the two systems and the second considers this interaction by the addition, to every support point on the PS, of a single-supported or multi-supported SDOF system. The structural responses are obtained by the direct integration of the Primary System equations of motion subjected to two simultaneous design acceleration time-histories, in the horizontal and vertical directions. The results are analyzed and compared to identify the general trends of the solutions obtained by the two types of analysis, and to detect their effects on the SS response. The study is concerned, also, with the importance of nonlinearities concentrated in the pipeline supports; in the case of the Brazilian nuclear power plants.