We have measured the thermopower and resistivity of two series of cuprate superconductor, Tl0.5Pb0.5Sr2−xLaxCuO5and Bi2Sr2−xLaxCuO6+ywhich possess a single CuO2plane. In each series, the hole concentration can be varied by changing the La content, permitting investigation of the overdoped, maximum-Tcand underdoped regimes. The thermopower follows a pattern similar to that seen in superconductor series with more than one CuO2plane, namely an approximately linear decrease as temperature increases well above Tc. However, the thermopower shows a minimum above Tcfollowed by a maximum as temperature increases for samples with a small thermopower and high Tc. The magnitude of thermopower as a function of Tcis in general agreement with the universal behaviour found for other cuprate superconductors. © 1994 IOP Publishing Ltd. © 1994 IOP Publishing Ltd.