Rate constants have been measured for vibration to vibration energy transfer from (CO)-C-12-O-16(v = 1) to the first vibrationally excited state of both (CO)-C-13-O-16 ( = 47 cm(-1)) and (CO)-C-13-O-18 ( = 100 cm(-1)) using the infrared laser fluorescence technique over the temperature range 50 to 270 K in the gas phase and in liquid neon, deuterium and argon solutions. Fluorescence from (CO)-C-12-O-16(v = 1) was filtered out, and the time-dependence of the fluorescence intensity from the other isotopomer used to determine the rate constants for energy transfer. The results for the two isotopomeric systems are markedly different. For that with the smaller energy mismatch, (CO)-C-12-O-16 - (CO)-C-13-O-16, the rate constants increase with decrease in temperature from 270 to 80 K. This is shown to be consistent with near-resonant energy transfer mediated by transition dipole-transition dipole couplings. Below 80 K, the temperature dependence of the rate constants flattens. For the (CO)-C-12-O-16 - (CO)-C-13-O-18 system, the rate constants decrease with decrease in temperature from 270 to 100 K, below which they increase with further decrease in temperature. The temperature dependence in the range 270 to 100 K is shown to be consistent with energy transfer mediated by a combination of by long range and short range forces. Below 100 K, the temperature dependence of the rate constants is governed by attractive forces which influence the collision pair during their encounter. The rate constants are compared with previous studies of near-resonant vibrational energy transfer in other systems at low temperatures.