This paper considers the solution of systems of algebraic equations that are expressed by a global rectangular system of equations, and a set of conditional equations that are expressed as disjunctions. These disjunctions are given by equations and inequalities, where the latter define the domain of validity of the equations. The solution of such a system is defined by variable values satisfying the rectangular equations, and exactly one set of equations for each of the disjunctions. This paper addresses first the solution of systems of linear disjunctive equations. Using a convex hull representation of each of the disjunctions, it is shown that these equations can be converted into an MILP problem. A sufficient condition is presented under which this model is shown to be solvable as an LP problem. An extension to nonlinear disjunctive equations is presented by incorporating the proposed MILP formulation within a Newton iterative scheme. The application of the proposed algorithms is illustrated with several examples, including piecewise linear mass balances in process networks, and pipe networks with different flow regimes and check valves. (C) 1998 Elsevier Science Ltd. All rights reserved.