A class of queueing networks which consist of single-server fork-join nodes with both infinite and finite buffers is examined to derive a representation of the network dynamics in terms of max-plus algebra. For the networks, we present a common dynamic state equation which relates the departure epochs of customers from the network nodes in an explicit vector form determined by a state transition matrix, and give related examples. Finally, applications of the representation to the analysis and simulation of queueing networks are briefly discussed.