The transformations between ITRFXX (International Terrestrial Reference Frame) established for local and regional geodetic networks and ED50 (European Datum 1950) are routinely implemented in practice via several transformation models. In some specific cases, these models, which are widely used in practice, may be insufficient to solve the transformation problem, and thus this causes a significant loss of accuracy for the transformed points coordinates. In this study, firstly the polynomial transformations with general equations (GP) and complex numbers (CNP) were examined as alternative to well-known transformation models for modelling the distortions. In addition, transformation models based on radial basis functions (RBFs), a modern method for estimating multivariable functions, have been examined. The transformation problem has been addressed in two numerical case studies, with real data located in different regions of Turkey.