The membership of eight cluster Cepheids,DL Cas,EV Sct, V367 Sct, S Nor, TW Nor,V340 Nor, U Sgr and CS Vel, has been examined by comparing their systemic radial velocity with that observed for the red giants in the same clusters. The membership is very probable in seven cases, the only-exception being CS Vel. Additional observations of main sequence stars are necessary to confirm some of the conclusions. One spectroscopic binary was discovered among the Cepheids (DL Cas) and at least four were among the red giants. Orbits have been determined for two red giants, one in NGC 129 and one in IC 4725. The position within the instability strip of the nonvariable F5Ib star in NGC 129 is due to its probable composite (gK + dB) character. The ratio of the number of Cepheids to the number of red giants is less than 1, in good agreement with the prediction of evolutionary models with core overshooting. This study is based on 382 observations of 45 stars, obtained with the radial velocity scanner CORAVEL.