In the present work, based on experimental investigations of reaction propagation in Ta-N and Ti-N systems, we show that infiltration plays a key role in the mechanism of spin mode combustion. The influence of two main parameters of infiltration combustion, initial sample density (rho) and reactant gas pressure (P), was investigated. Based on the results, pressure-density (P-rho) diagrams are constructed, which present the regions of different wave propagation behavior. For example, it is shown that for both systems a range of nitrogen pressure exists where by increasing initial sample density one passes from spin to steady planar mode, with decrease of combustion velocity. Also, for a range of rho, decrease of P leads to combustion limit without observation of spin or oscillation modes. Further. it is shown that the phase composition of products depends on the combustion mode. A variety of questions arise from this work. While qualitative explanations are provided in this paper, we believe that quantitative answers to these and other questions may be obtained only from models that account for infiltration and the heterogeneous nature of the process.