We present XKD, a novel self-supervised framework to learn meaningful representations from unlabelled video clips. XKD is trained with two pseudo tasks. First, masked data reconstruction is performed to learn modality-specific representations. Next, self-supervised cross-modal knowledge distillation is performed between the two modalities through teacher-student setups to learn complementary information. To identify the most effective information to transfer and also to tackle the domain gap between audio and visual modalities which could hinder knowledge transfer, we introduce a domain alignment strategy for effective cross-modal distillation. Lastly, to develop a general-purpose solution capable of handling both audio and visual streams, a modality-agnostic variant of our proposed framework is introduced, which uses the same backbone for both audio and visual modalities. Our proposed cross-modal knowledge distillation improves linear evaluation top-1 accuracy of video action classification by 8.4% on UCF101, 8.1% on HMDB51, 13.8% on Kinetics-Sound, and 14.2% on Kinetics400. Additionally, our modality-agnostic variant shows promising results in developing a general-purpose network capable of handling different data streams.