Convolutional network coding deals with the propagation of a message pipeline through a cyclic network. We formulate a convolutional network code by associating every pair of adjacent channels with a rational power series over the base field, called the local encoding kernel, and every channel with a concomitant global encoding kernel, which is a vector of rational power series. Given a complete set of local encoding kernels, a close-form formula is derived for calculating the global encoding kernels. A convolutional multicast is a convolutional network code that every qualified receiving node can decode the message. We offer a construction algorithm for a convolutional multicast as well as a decoding algorithm.