We develop a time-varying normalizing flow (TVNF) for explicit generative modeling of dynamical signals. Being explicit, it can generate samples of dynamical signals, and compute the likelihood of a (given) dynamical signal sample. In the proposed model, signal flow in the layers of the normalizing flow is a function of time, which is realized using an encoded representation that is the output of a recurrent neural network (RNN). Given a set of dynamical signals, the parameters of TVNF are learned according to a maximum-likelihood approach in conjunction with gradient descent (backpropagation). Use of the proposed model is illustrated for a toy application scenario-maximum-likelihood based speech-phone classification task.