Effects of the higher-order harmonics in the d-wave gap function have recently been suggested by some experiments on high-'Tc' superconductors. For some materials, the electron-doped ones for example, the properties calculated using only the first harmonic in the d-wave gap do not agree with the experiments. By including the effects of higher-order harmonics, we can reproduce variations in the d-wave gap symmetry, such as the non-monotonic variations revealed by electronic Raman scattering (G. Blumberg ' et al.' 2002). We investigate the effects of those harmonics, in the cases of a circular Fermi surface and a tight-binding Fermi surface, by calculating important properties such as the temperature-dependent penetration depth, the electronic Raman response functions, the energy-dependent density of states, the specific heat jump at 'Tc', and the gap ratio.