A μSR study of the temperature dependence of the London penetration depth λ in sintered samples of YBa2Cu3Oz (with various oxygen contents x), YBa2Cu4O8 and Bi2Sr2CaCu2O8 is presented. It is found that the temperature behavior of λ of all these cuprate superconductors is consistent with conventional s-wave pairing. However, there are significant differences concerning the exact temperature dependence of λ in these materials. In YBa2Cu3Oz with high x, the behavior of λ(T) is well described by the two-fluid model (strong coupling), whereas λ(T) in YBa2Cu3Oz with low x, YBa2Cu4O8 and Bi2Sr2CaCu2O8 is in better agreement with weak-coupling BCS theory. Possible reasons for the different temperature behavior of λ in these materials are discussed. © 1991.