AbstractMomentum relaxation times and ohmic mobilities are calculated for a quasi‐one‐dimensional (QID) semiconducting system assuming that carriers are scattered by acoustic and piezoelectric phonons. A detailed discussion of inter‐sub‐band transitions is done with special emphasis on the conditions where size‐quantum‐limit (SQL) is accomplished. A comparison of the acoustic and piezoelectric mechanisms is done for GaAs and CdS with detailed analysis of which mechanism dominates transport under given conditions. The temperature dependence of the mobilities is also discussed and asymptotic analytical expressions are obtained for the low temperature regime.