Complex surfaces have been classified by Kodaira in I of [12] up to birational isomorphism. In this note we study effective smooth circle and torus actions on complex surfaces. In §1 we consider actions on ruled surfaces, Enriques surfaces and the elliptic modular surface BΓ_(3)^＋ The series of elliptic modular surfaces BΓ_(N) (N≧5) belong to the class IV_0 and some family of elliptic surfaces derived from basic ones are in the class IV_0 or VI_0 ([1l]). Actions on these surfaces are considered in § 2. Hopf sufaces and Inoue surfaces [8] are in the class VII_0. In §3 we study actions on these surfaces. In this note we mean by an action an effective action.