Systems of iterative functional equations with a non-trivial set of contact points are not necessarily solvable, as the resulting intersections may lead to an overdetermination of the system. To obtain existence and uniqueness results additional conditions must be imposed on the system. These are the compatibility conditions, which we define and study in a general setting. An application to the affine and doubly affine cases allows us to solve an open problem in the theory of functional equations. In the last section we consider a special problem in a different perspective, showing that a complex compatibility condition may result in an elegant and simple property of the solution.

具有非平凡的一组接触点的迭代功能方程组不一定是可解的，因为所产生的交点可能导致系统的确定性过高。为了获得存在和唯一性结果，必须对系统施加附加条件。这些是兼容性条件，我们在一般情况下定义和研究。在仿射和双重仿射情况下的应用使我们能够解决泛函方程理论中的一个开放问题。在上一节中，我们从不同的角度考虑了一个特殊的问题，表明复杂的兼容性条件可能会导致解决方案优雅而简单。