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SUMMARY Numerical solution of dynamic problems requires accurate temporal discretization schemes. So far, to the best of the authors' knowledge, none have been proposed for adhesive contact problems. In this work, an energy-momentum-conserving temporal discretization scheme for adhesive contact problems is proposed. A contact criterion is also proposed to distinguish between adhesion-dominated and impact-dominated contact behaviors. An adhesion formulation is considered, which is suitable to describe a large class of interaction mechanisms including van der Waals adhesion and cohesive zone modeling. The current formulation is frictionless, and no dissipation is considered. Performance of the proposed scheme is compared with other schemes. The proposed scheme involves very little extra computational overhead. It is shown that the proposed new temporal discretization scheme leads to major accuracy gains both for single-degree-of-freedom and multi-degree-of-freedom systems. The single-degree-of-freedom system is critically analyzed for various parameters affecting the response. For the multi-degree-of-freedom system, the effect of the time step and mesh discretization on the solution is also studied using the proposed scheme. It is further shown that a temporal discretization scheme based on the principle of energy conservation is not sufficient to obtain a convergent solution. Results with higher order contact finite elements for discretizing the contact area are also discussed. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]