In this work sufficient time-varying conditions were established for assuring local persistent excitation for identification of a large class of nonlinearly parametrized model structures under integral cost functionals of arbitrary degree. The conditions are algebraic in nature. They can be set up off-line in a symbolic form and evaluated on-line. The potential benefit of these conditions mainly reclines in the design of excitations for nonlinear system identification. A simple method for optimal input design is presented. Examples illustrate the features of the approach.