This document discusses recommendations made by FRAME and the Royal Commission on Environmental Pollution (RCEP) with regard to the current European Commission proposals on the Registration, Evaluation and Authorisation of Chemicals (REACH) system for assessing the risks of chemicals to humans, wildlife and the environment. Of several common aims and recommendations, the two most important are: a) the greater use of non-animal testing methods, especially computational prediction methods (for example, [quantitative] structure-activity relationships, expert systems and biokinetic modelling) for prioritising chemicals for hazard assessment; and b) the greater use of intelligent exposure-based targeted risk assessment, with less emphasis being placed on tonnage-triggers. FRAME has produced a decision-tree testing scheme to illustrate the way in which these approaches could be used, together with in vitro test methods. This scheme has been slightly modified to take account of proposals subsequently made by the RCEP. In addition, FRAME points out that new and improved computational methods are needed through more coordinated research, and that these and existing methods need to be validated. The similarities between the independent publications of FRAME and the RCEP add weight to the recommendations that each have made concerning the implementation of the REACH system.