We address the problems of almost asymptotic stabilization and global asymptotic regulation (GAR) for a class of high-order nonholonomic systems in power chained form. This particular class of nonlinear systems is an extension of a nonholonomic system in chained form that has received considerable attention in the past few years. The nonholonomic system considered in this note is not necessarily affine in the control variables and therefore cannot be handled by existing methods. Sufficient conditions are presented under which a discontinuous state feedback control law (respectively, a switching controller) can be recursively constructed, using the so-called adding a power integrator technique proposed in [17], [18]. We also illustrate how the results can be extend to multi-input systems in power chained form. Simulation examples are provided to demonstrate effectiveness of the proposed controllers.