We provide a general procedure to calculate the current-induced spin-transfer torque which acts on a general steep magnetic texture due to the exchange interaction with an applied spin-polarized current. As an example, we consider a one-dimensional ferromagnetic quantum wire and also include a Rashba spin-orbit interaction. The spin-transfer torque becomes generally spatially nonlocal. Likewise, the Rashba spin-orbit interaction induces a spatially nonlocal fieldlike nonequilibrium spin-transfer torque. We also find a spatially varying nonadiabaticity parameter and markedly different domain wall dynamics for very steep textures as compared to wide domain walls.