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Bidirectional coronal type III bursts are modeled by combining a model of coronal electron heating and beam generation via time-of-flight effects with semiquantitative estimates of quasilinear relaxation. Electromagnetic emissivities are estimated by extending the recently developed theory of interplanetary type III bursts to coronal emissions, including its features of stochastic Langmuir-wave growth and three-wave interactions. The results are investigated for heating on open and closed coronal field lines and are compared with observations of normal, reverse-slope, bidirectional, and inverted-J and -U coronal type III radio bursts. Harmonic emission is predicted to dominate at plasma frequencies above roughly 100 MHz where the efficiency of fundamental emission falls off steeply, while its free-free reabsorption rises. The model also explains the observed trends in the likelihood of occurrence of normal, reverse-slope, and bidirectional coronal type III bursts.