This paper extends the A* methodology to shortest path problems in dynamic networks, in which arc travel times are time dependent. We present efficient adaptations of the A* algorithm for computing fastest (minimum travel time) paths from one origin node to one destination node, for one as well as multiple departure times at the origin node, in a class of dynamic networks the link travel times of which satisfy the first-in-first-out property. We summarize useful properties of dynamic networks and develop improved lower bounds on minimum travel times. These lower bounds are exploited in designing efficient adaptations of the A* algorithm to solve instances of the one-to-one dynamic fastest path problem. The developed algorithms are implemented and their computational performance is analyzed experimentally. The performance of the computer implementations of the adaptations of the A* algorithm are compared to a dynamic adaptation of Dijkstra's algorithm, stopped when the destination node is selected. Comparative computational results obtained demonstrate that the algorithms of this paper are efficient. Using a network containing 3000 nodes, 10 000 links, and 100 time intervals, the dynamic adaptations of the A* led to a savings ratio of 11, in terms of number of nodes selected, and to a savings ratio of five in terms of computation time. The effect of the network size on the performance of these adaptations is also studied. It is shown that the computational savings in term of both the number of nodes selected and the computation time, increase with the size of the network topology.