There are three important aspects which must be taken into account when the problem of stability of long-range cooperative agreements is investigated: time-consistency of the cooperative agreements, strategic stability and irrational behavior proofness. The mathematical results based on imputation distribution procedures (IDP) are developed to deal with the above mentioned aspects of cooperation. We proved that for a special class of differential games time-consistent cooperative agreement can be strategically supported by Nash equilibrium. We also consider an example where all three conditions are satisfied