In this project basically theory and algorithms for a single commodity rnow problemsrnsimultaneously optimizing two objectives ( Biobjective ) are addressed. For both con-rntinuous and integer case methods like Biobjective network simplex method, two phasernmethod and weighted metric methods are presented to compute the complete set ofrnecient solution in the objective space . In addition to these main ideas, the projectrnalso explains some points about multiobjective optimization problem and network rnowrnproblems.rnKeywords: Network programming; Biobjective minimum cost rnow problem; Ecientrnextreme points; Biobjective Network simplex method; Two phase method; weightedrnmetric method