We present DynHair, a novel method for tracking and modeling dynamic hair for human head avatars. From video input, we reconstruct a dynamic head avatar with an explicit strand-based hair representation using structured 3D Gaussian Splatting. In contrast to the face region of human head avatars, which can be modeled with 3D Gaussians that are attached or generated with respect to some expressive 3D head model, hair is particularly challenging as it exhibits dynamic motion effects. Therefore, we present a novel method that models the dynamic deformations of the hair strands using a temporal network that is conditioned on angular velocity and acceleration of the head, as well as relative gravity. Specifically, an LSTM encodes the motion history and modulates per-point strand features via FiLM conditioning which further used by MLP to produce physically plausible displacements to canonical hairstyle. We jointly optimize this motion and appearance representation of the hair, with a 3DGS-based representation of the face-region, via differentiable Gaussian splatting with photometric, geometric, and physics-based supervision. As a result of our method, we retrieve hair tracking of the training video data and an animatable head avatar with controllable hair dynamics. In our experiments, we demonstrate state-of-the-art performance in terms of hair dynamics, temporal consistency, and generalization across subjects.