The stabilization problem for nonlinear dynamical systems under zero-state-detectability assumption or its analogues is considered. The proposed solution ensures finite time practical stabilization of the system and it is based on uniting local and global controllers for the system. The global controller provides boundedness of the system solutions and output convergence to zero, while local one ensures finite time convergence to a prescribed goal set inside the zero dynamics set. Computer simulation demonstrates potentiality of the proposed solution.