The strain-induced director reorientation process in nematic liquid single crystal elastomers is investigated for the case of an arbitrary angle between the original director and the external stress axis. If the mechanical stress is applied perpendicular to the original director axis, the reorientation process sets in at a threshold strain. The mesogens are realigning 'clockwise' or 'counter-clockwise' towards the axis of external stress, simultaniously the monodomain structure is distorted and a periodic pattern formation is observed. If the mechanical stress is applied obliquely with respect to the original director axis, a uniform director reorientation is obtained with retention of the monodomain structure. No threshold strain is observed for this process. The existence of a threshold strain in the case of a perpendicular arrangement of the director to the external stress axis can be understood as a consequence of the distortion of the monodomain structure.