The transverse Kerr effect (TKE) has been measured in amorphous R-Co thin film alloys, in fields up to 2 T and at temperatures between 17 and 200 K. In such measurements, the change of relative reflectivity (DELTA-R/R)s is related to the spontaneous magnetisation M(s) through the proportionality constant K(TKE) = (DELTA-R/R)/M(s). IN Y-Co alloys, K(KTE) is approximately temperature independent and equal to 12 x 10(-6) emu cm-3. In R-Co alloys, where R = Nd, Gd or Er, the respective contributions of R and Co atoms to the total Kerr signal, DELTA-R/R(tot)(T), have been deduced from the comparison between the temperature dependences of DELTA-R/R(tot)(T) and M(s)(T). It was found that the Co contribution is largely dominant over the R ones and that the Nd contribution is larger than that of Gd and Er. These behaviours are consistent with those characterizing the Kerr rotation in these different alloys.