The influences of compositional asymmetry on the two-photon photoluminescence and the second harmonic generation processes in weakly coupled plasmonic dimers were addressed. Au-Au homodimer and Au-Ag heterodimer arrays produced using electron-beam lithography were investigated using confocal nonlinear optical imaging and spectroscopy. Compared to the Au-Au homodimers, the Au-Ag dimers showed slightly broadened two-photon photoluminescence near the X symmetry point at the first Brillouin zone of Au, whilst that from the L symmetry point stayed the same. Additionally, weakly coupled Au-Ag heterodimers generated strong second harmonic signals which were invisible in the Au-Au homodimers. The observations highlighted the importance of compositional asymmetry in the non-linear optical studies of plasmonic dimers.