We consider tractable and intractable cases of the satisfiability problem for conjunctions of inequalities between variables and constants in a fixed finite poset. We show that crowns are intractable. We study members and closure properties of the class of tractable posets. We define a feasible poset to be one whose potential obstacles to satisfiability are representable by a certain formula of the first-order extended by the least fixed operator. For bipartite posets we give a complete classification of hard posets and feasible ones.