Dependence of transformation temperatures of ternary and quaternary NiTi-based shape memory alloys on the number (e(v)/a) and concentration (c(v)) of valence electrons is investigated. Two distinct trends of transformation temperatures with respect to the number of valence electrons per atom are found depending on whether e(v)/a=7 or e(v)/la not equal 7. Clear correlations between transformation temperatures and c(v) exist. M-s and A(s) decrease consistently from 900 to -100 degrees C, and 950 to -30 degrees C, respectively, with increasing cv from 0.145 to 0.296. The relationship of electron concentration on the elastic moduli of the NiTi-based alloys is discussed. The possible influence of the atomic size of alloying elements on transformation hysteresis is introduced.