(12) C / (13) C line intensity ratios have been derived from several carbon-bearing molecules to confine the range of carbon and oxygen isotope abundance ratios toward the nuclear regions of two infrared bright galaxies. The most stringent limits are obtained from CN mm-wave emission lines. Supplementary measurements toward the Galactic center region indicate that overall I(twCN)/I(thCN) line intensity ratios are giving lower limits to the corresponding ISOC abundance ratio. Toward M82 and IC342, we find ISOC > 40 and > 30. Therefore the smaller ISOC ratio of our own Galactic center region (25) may not be typical for central regions of galaxies which are more luminous in the infrared. The ISOC limits and data from various isotopic species of CO also infer ISOA abundance ratios of > 90 and > 125 for M82 and IC342, respectively. From the I(HCfoN) / I(HCfiN) line intensity ratio, ISON > 100 is derived for M82. Based on observations with the IRAM 30-m telescope, Pico Veleta, Spain and the Swedish-ESO Submillimetre Telescope (SEST) at the European Southern Observatory (ESO), La Silla, Chile