An investigation has been carried out on the texture of Ti-44Ni-5Cu (at %) shape memory alloy wire. The texture of the B2 and monoclinic phases has been determined as a function of the degree of cold deformation during the drawing process and the number of cycles on thermomechanical cycling. After cold drawing and anlealing (823 K, 180 s) under tensile stress, the , [1(-1)0]  and [(-1)01] directions in the monoclinic phase are parallel to the wire axis. In this condition a preference for the [(-1)01] component is observed. On heating the wire above Af and cooling down, this preference disappears. Subsequently the preference develops again on thermomechanical cycling. The B2 phase shows in all conditions a <111> fiber texture. The observed preference of the [(-1)01] fiber texture component in the monoclinic phase is discussed in terms of strain accomodation during plastic deformation.