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Joint radar–communications (JRC) waveform could enable simultaneously radar sensing and communication functions in a multifunction integrated system (MFIS). Because of the special JRC waveform characteristics of MFIS, the traditional task scheduling algorithm for multifunction phased array radar cannot be applied to the MFIS to release its full potential. Therefore, a novel adaptive task scheduling algorithm for JRC waveform enabled MFIS is proposed in the paper. Firstly, the modified JRC waveform scheduling criteria for MFIS are remodeled after establishing the multi-task models. Secondly, the task scheduling optimization problem, which can reflect the scheduling capability of the JRC waveform, is reformulated, and the proposed novel adaptive task scheduling algorithm based on the JRC waveform effectively schedules different kinds of tasks. Finally, the simulation results show that the proposed algorithm not only has a high JRC waveform scheduling capability but also provides better performance compared with the traditional ones.