Processing children’s speech is challenging due to high speaker variability arising from vocal tract size and scarce amounts of publicly available linguistic resources. In this work, we tackle such challenges by proposing an unsupervised feature adaptation approach based on adversarial multi-task training in a neural framework. A front-end feature transformation module is positioned prior to an acoustic model trained on adult speech (1) to leverage on the readily available linguistic resources on adult speech or existing models, and (2) to reduce the acoustic mismatch between child and adult speech. Experimental results demonstrate that our proposed approach consistently outperforms established baselines trained on adult speech across a variety of tasks ranging from speech recognition to pronunciation assessment and fluency score prediction.