The main concern of this work is with the application of the modal spectral seismic analysis to secondary structural systems of nuclear power plants, with the large amount of conservatism which is included in them, and, of course, with the consequences to the particular case of the plants under construction in Brazil. One considers the design analysis methods which have been used so far in Brazil, as well as the most recent developments in the area, in USA and in Europe, to conclude about the adequacy of those procedures and recommend eventual changes to them. One then studies the subjects of the coupling effect between the primary and secondary system responses, the influence of the piping support relative displacements, the contribution of the cross-correlation among response modal components and the participation in the overall response of the so-called rigid modes. The main computer program aid is taken from an ANSYS-2 version and one uses a reduced model of a piping system as the secondary system and a 3-D beam element model of a reactor building as the primary system. The spectral analysis results are compared to time domain solutions using the same structural models excited by a design accelerogram. Conclusions and recommendations are oriented to the present design practice in Brazil.