Summary In recent years, such conjugate-gradient-type methods as orthomin have been used very successfully with various preconditioners to solve the unsymmetric linear systems that arise in reservoir simulation. Here these successful iterative methods are combined with a new set of preconditioners that have been derived from some powerful algorithms in direct sparse Gaussian elimination. The SPARSPAK implementations of minimum degree and nested dissection algorithms have been modified to yield incomplete LU factorizations. Their application to reservoir simulation problems is investigated here.