New methods of the Padé and Chebyshev type are applied to the solution of the point kinetics equations. In Sec. I, a theoretical analysis is presented in an attempt to derive global approximations by opposition to the local ones that have been used up to now. It is shown that many of the techniques developed earlier for integrating stiff systems of ordinary differential equations are particular cases of our general formalism. In Sec. II, numerical studies are presented for various reactivity insertions. The results confirm the theoretical analysis and indicate the range of applicability of the methods presented.