The shape memory alloys (SMA) are a group of materials which have the ability of recovering a pre-memorized shape when submitted to a suitable heat treatment. The shape memory effect (SME) is due to a structural change from a low symmetry, low temperature structure (capable of absorbing a great amount of recoverable deformation) to a cubic structure, stable at a higher temperature; the reverse deformation takes then place due to the higher rigidity of the structure of the highest temperature. The NiTi system is the most popular of the SMA's because of the considerable work per unit mass it can produce during recovery, and because of the value of the transformation temperature (from - 50 to + 100degreesC) and of its good oxidation resistance. The goal of the present work is to study the influence of thermal cycling on the transformation temperatures of a Ti-rich alloy with average composition of Ni-51at% Ti (most studies in the literature concern the Ni-rich alloys). Using differential scanning calorimetry (DSC), it is possible to identify the transformation temperatures and the phases present in the alloy after the thermal cycling. Changing the heat and cooling rates and also the soaking times and temperatures of the cycles, it will be possible to reach the goals proposed. The evolution of the transformation temperatures as a function of the heat treatment conditions is correlated with the structural changes that take place. In the present paper we discuss the effect of thermal cycles on the relative relevance of the R-phase peak as detected by DSC and its correlation with Ms/Mf temperatures.