Translational energy dependences of relative cross sections for Hg(6(3)P(1) --> 6(3)P(0)) fine-structure changing collisions with N-2 and CO have been measured with a crossed-beam apparatus over the energy range between 800 and 3750 cm(-1). A negative energy dependence is obtained for Hg-CO, but a positive energy dependence is observed for Hg-N-2, with an energy threshold for appearance of Hg(6(3)P(0)) around 900 cm(-1). These results are explained using the characteristics of the intermolecular potentials for Hg-N-2 and Hg-CO. The existence of the energy threshold around 900 cm(-1) for N-2 suggests simultaneous vibrational excitation of N-2. The translational energy dependence has also been measured under beam-gas conditions over the energy range between 450 and 3350 cm(-1). From a comparison with Hg(6(3)P(1) --> 6(3)P(0)) intramultiplet deactivation cross sections for HE-N-2 and Hg-CO obtained in gas cell experiments, absolute values of the cross sections for this intramultiplet transition are estimated as a function of the average translational energy under the beam-gas conditions. There is no clear threshold for Hg-N2 in the beam-gas experiment and it is suggested that a higher rotational temperature of N-2 induces a shift of the energy threshold effectively lower.