We report on the shear-induced transition from an oriented lamellar phase (L, phase) to multilamellar vesicles (MLV) in two nonionic surfactant systems, namely, a 40 wt % sample of triethylene glycol monodecyl ether (C10E3) and a 40 wt % sample of tetraethylene glycol monododecyl ether (C12E4) in D2O. This transition was studied by time-resolved small-angle neutron and light scattering under shear. Within a range of shear rates from 2 to 100 s(-1) at 25 degreesC the transition from the L-alpha, phase to MLVs in the C10E3 system apparently is controlled by strain. This transition involves an intermediate structure with cylindrical scattering symmetry. This can be interpreted as multilamellar cylinders (MLCs) or as a coherent stripe buckling with the wave vector of the undulation in a neutral direction. The intermediate structures found along the transition path are stable for long times, when shear is turned off. This allows for studies on trapped intermediate structures and experiments where different positions within the gap of a couette shear cell were examined in so-called gap-scan experiments. These experiments revealed that the transition from planar lainellae to MLVs is homogeneous throughout the gap. A temperature increase to 32 degreesC changes neither the pathway nor the strain control in comparison with experiments run at 25 degreesC. Upon a further increase in temperature to 38 degreesC, the transition leads to a mixture of MLC and planar lamellae or a weakly buckled state. With C12E4 as surfactant, and therefore with changed bilayer properties, a strain control is still observed, but less strain is needed for the transition compared to that of the C10E3 system. A comparison of the transition for the two systems, their transient as well as their steady-state viscosities, indicates that the transition is controlled by the stress.