Sufficient conditions for the local convergence and necessary and sufficient conditions for the Q-superlinear convergence of two classes of methods for least squares estimation are given. These classes of methods are referred to as classes B and C, and the related class of methods which is decribed by Pereyra (1967) is referred to as class A. Composite methods are constructed from a class A method and a class B method, and from a class A method and a class C method respectively, and numerical results for the class A method and for the two composite methods are presented for eleven test problems.