T. Global in time solutions of the equations Ou = H(u, u') on Minkowski space-time are considered. Results available so far involve complicated decay and energy estimates and also careful choice of Banach spaces and associated ordinary differential inequalities. This work tries to simplify some of the existing arguments and to develop a new technique for other nonlinear evolution equations. The method is motivated by the work of Christodoulou and Baez, Segal, and Zhou, on nonlinear wave equations. The key idea is to use the Penrose conformal compactification that transforms the equations from Minkowski space to the Einstein universe in order to change the global existence question to the local one.