A micromechanics-inspired constitutive model is developed to describe the deformation behaviour of fibrillated material within crazes in glassy polymers subjected to cyclic loading. In a finite strain setting, the model accounts for the morphology change taking place by the drawing of material from the intact bulk polymer into craze fibrils and their transition from primitive to mature fibrils. Building on previous research, fibril drawing is described as a viscoplastic process. A novel contribution of this study is the incorporation of viscoelastic deformation of existing fibrils, which is motivated by experimental observations. This new perspective allows for creep recovery, especially during the unloading phases of cyclic deformation.A parameter study which pays special attention to the role of the characteristic times scales of fibril drawing and fibril creep in relation to the imposed loading rate illustrates the performance of the model. Since the model is designed as an input to cohesive fracture simulations in glassy polymers, its response under monotonic loading is analysed and compared to existing crazing models. Of primary interest, however, is the model behaviour under cyclic loading which is investigated for different loading scenarios up to fibril failure. The study highlights the complex interplay between the two viscous mechanisms and how they influence the local deformation behaviour of the craze matter as well as the number of cycles until failure.