Abstract. The complementary principle is an important methodology for estimating evaporation. Throughout the 56-year development, related studies have shifted from adopting a symmetric linear complementary relationship (CR) to employing generalized nonlinear functions. Studies based on the linear CR have been maintained for a long time by rationally formulating the potential (E_po) and apparent potential evaporation (E_p) and/or employing an asymmetric parameter. These works have also advanced two types of generalized nonlinear complementary functions by invoking the boundary conditions. The first type inherits the concepts of three types of evaporation yet still requires the prognostic modelling of E_po. Polynomial functions are derived and tested for this type of function. Meanwhile, the second type does not involve E_po, yet requires a diagnostic modelling of actual evaporation by using the radiation and aerodynamic components of the Penman (1948) equation as inputs. A sigmoid function is derived by satisfying the boundary conditions based on physical considerations. The generalized nonlinear functional approach has improved the understandings on the complementary principle, and shows potential in advancing the evaporation research. Further studies may cover several topics including boundary conditions, analytical forms, parameterization, and application.