For cooperative-antagonistic networks, the distributed control problem is solved owing to all static interactions among vertices, expressed conveniently by a communication graph whose edge weights are constant or time-varying numbers. The question asked in this paper is: whether and how can distributed control be achieved in the presence of dynamic interactions that are modeled as edge weights in terms of transfer functions on a communication graph? The answer is affirmative, and the nearest neighbor rule is effective for designing dynamic distributed controllers. Necessary and sufficient conditions are given for convergence of cooperative-antagonistic networks which can admit hybrid static and dynamic interactions. By defining a class of dynamic signed graphs and the related sign-indicator matrices, the structural balance/unbalance is proposed to describe the convergence conditions under dynamic interactions. Examples are provided to validate structure properties and convergence results of cooperative-antagonistic networks with dynamic interactions.