We study the dynamics of quantum and classical correlations in the presence of nondissipative decoherence. We discover a class of initial states for which the quantum correlations, quantified by the quantum discord, are not destroyed by decoherence for times t<t¯ . In this initial time interval classical correlations decay. For t>t¯ , on the other hand, classical correlations do not change in time and only quantum correlations are lost due to the interaction with the environment. Therefore, at the transition time t¯ the open system dynamics exhibits a sudden transition from classical to quantum decoherence regime.