We establish a general principle on the boundedness of operators on local Orlicz-Morrey spaces. As applications of this principle, we obtain the boundedness of the Calderón-Zygmund operators, the nonlinear commutators of the Calderón-Zygmund operators, the oscillatory singular integral operators, the singular integral operators with rough kernels and the Marcinkiewicz integrals on the local Orlicz-Morrey spaces