Current-voltage measurements show that C-60/n-GaN, C-70/n-GaN and C-70/p-GaN contacts have very good rectification characteristics, however, the polarities of the forward biases for C-60/n-GaN (C-70/n-GaN) and C-70/p-GaN are opposite to each other. By fitting forward current-voltage data, the relations of both the series resistance and ideality factor vs forward bias for C-60/n-GaN and C-70/n-GaN have been obtained. Thermal activation measurements at a fixed forward bias reveal exponential relations of currents vs the reciprocal of temperature. The effective barrier heights for C-60/n-GaN and C-70/n-GaN are determined to be 0.535 and 0.431 eV, respectively.