Intensive investigations have been carried out on CuAlNiTi shape memory alloys (SMAs) with 1 wt.%Ti and Ni content from 5 to 6 wt%, In this present work, we used a rapid solidification technique to prepare alloys of two compositions: (wt%) Cu79Al13Ni5Ti2Si1, Cu79Al13Ni5Ti1Nb2. The ribbons obtained were characterised by means of XRD, DSC measurements and TEM observations. XRD patterns indicated that the first alloy has a two-phase structure with beta and martensite 18R phases, whereas the second one is only beta. DSC measurements gave characteristic transformations temperatures. The Si-containing alloy showed low temperature transformations with M-s about -88degreesC and A(f) at -41degreesC in as-quenched state. The Nb-containing alloy exhibited high temperature transformations with A(f) about 170degreesC in the as-quenched state, which is quite higher for this alloy family. The transformation temperatures are stabilised after only one cycle at DeltaT(M)=(M-s-M-f) constant for both alloys. This stabilisation is likely to be generated, in the case of Cu79Al13Ni5Ti1Nb2, by nanocrystalline precipitates revealed on TEM micrographs. Narrow and faulted martensite plates have been observed in agreement with previous results on rapidly solidified CuAlNiTi SMAs.