The Ruderman–Kittel–Kasuya–Yosida (RKKY) exchange interaction is investigated for the first time in compounds of binary REM (rare-earth metal) – In systems (REМ = Gd, Tb, Dy, Ho, Er, or Тm) using experimental values of the paramagnetic Curie temperature (θp ) of these compounds. The prediction of the RKKY theory on the direct proportionality between θp and the de Gennes factor for equiatomic compounds of heavy REM with indium, similarly to pure REM, is confirmed. Values of the indirect exchange interaction parameter are estimated semiempirically for the examined compounds. As a whole, it is established that for the compounds of REM with indium, as for pure REM, the exchange interaction of RKKY type is characteristic.