In this paper, optimization of a linear objective func-tion with fuzzy relational inequality constraints is in-vestigated where the feasible region is formed as the in-tersection of two inequality fuzzy systems and Dombi family of t-norms is considered as fuzzy composition. Dombi family of t-norms includes a parametric family of continuous strict t-norms, whose members are increas-ing functions of the parameter. This family of t-norms covers the whole spectrum of t-norms when the param-eter is changed from zero to in nity. The resolution of the feasible region of the problem is rstly investigated when it is de ned with max-Dombi composition. Based on some theoretical results, a necessary and su cient condition and three other necessary conditions are de-rived for determining the feasibility. Moreover, in order to simplify the problem, some procedures are presented.