One successful technique for improving the robustness of codes to solve algebraic nonlinear equations has been to use homotopies or continuation methods. The domains of interest, when solving real problems, are normally bounded. Furthermore, when procedures for evaluating physical properties are used, it is required that the parameters fed into the procedures belong to a bounded domain. The standard homotopies do not guarantee a bounded path, hence it may happen that the homotopy path goes outside a given domain. Bounded homotopies have been proposed recently (Paloschi, 1995) which guarantee a bounded path. These have a dense Jacobian, even when the original problem is sparse, hence they can not be used for sparse problems. The purpose of this paper is to extend the results of Paloschi (1995) for handling sparse problems. New homotopies are proposed ensuring a bounded path and having a Jacobian with the same sparsity pattern as the original problem. An implementation is proposed which does not increase considerably either the computation time or the storage. It is tested by using two examples. One consists of the simulation of a distillation column using Antoine coefficients and the other involves the design of a small network of heat exchangers.