We study the dynamics of quantum correlations of qubit–qutrit systems under various decoherent channels. It is shown that the multi-local and local decoherent channels bring different influences for the dynamics of quantum correlations measured by negativity, quantum discord and geometric discord, which depend on the initial state parameters and the properties of the decoherent channels. We put emphasis on the phenomena such as entanglement sudden death, sudden transition between classical and quantum decoherence and stable quantum discord and geometric discord.