Summary: This article states and solves the maximum parametric flow over time problem. The proposed approach consists in repeatedly finding the maximum dynamic flow in discrete dynamic networks, for a sequence of parameter values, in their increasing order. In each of its iterations, the algorithm computes both the maximum flow, by minimizing the transit time (quickest flow), and the new breakpoint for the maximum parametric dynamic flow value function. The dynamic flow is augmented along quickest paths from the source node to the sink node in the time-space network, avoiding the explicit time expansion of the network. The complexity of thealgorithm is presented and also an example is given on how the algorithm works.