The aim of this paper is to discuss the theoretical aspects of multiobjective fractional problems. We consider a class of multiobjective fractional optimization problems (FOP) with inequality and degenerate equality constraints in which the objective function and the inequality constraints are only locally Lipschitz. We give second-order necessary conditions for the existence of local weak Pareto minimum and strict local Pareto minimum of order two for (FOP). Then we establish Fritz-John type necessary conditions for local weak Pareto minimum to problem (FOP), meanwhile, by introducing two constraint qualifications, we prove that the Fritz-John type necessary conditions become the Kuhn-Tucker type. The applicability of our conclusions is illustrated with some examples.