The cross sections for the reactions 113In(n,2n) and (n,n') and 115In(n,n'), (n,p) and (n, alpha ) at 14 MeV, and 115In(n,2n) from 14 to 18 MeV were measured by the activation technique. Special emphasis was placed on the accuracy of the results, and so full experimental details are included. The correlations between the measurements are considered, these being especially important for 112m,gIn. Isomeric cross section ratios were measured at 14.3 MeV: sigma m/ sigma g=(4.32+or-0.20) for 113In(n,2n)112m,gIn and sigma m/ sigma g=(4.59+or-0.03) for 115In(n,2n)114m,gIn. The results were compared with other published values, which show a very wide spread so that these cross sections cannot be considered well known at the present time. During the course of this work half-lives were measured for 112gIn((14.97+or-0.10)min), 112mIn((20.56+or-0.06)min) and 114In((71.6+or-0.1)s). The decay scheme of 114mIn was investigated, and gamma -ray intensities and a total internal conversion coefficient of (5.101+or-0.061) for the 190 keV gamma ray were obtained. In the case of 112mIn arguments are presented to support the theoretical total internal conversion coefficient for the 156 keV gamma ray of 6.80.