We address the problem of strategically supported cooperation for linear-quadratic differential games with nontransferable payoffs. As an optimality principle, we study Pareto-optimal solutions. It is assumed that players use a payoff distribution procedure guaranteeing individual rationality of a cooperative solution over the entire game horizon. We prove that under these conditions a Pareto-optimal solution can be strategically supported by an ε-Nash equilibrium. An example is considered.