Transfer lines simply characterise the interrelationship of manufacturing stages with their buffers and they are used to model the key features of such manufacturing environments with simplifying assumptions. There is a vast literature on these systems, however, little has been done on the transient analysis of the transfer lines by making use of the higher order moments of their performance measures due to the difficulty in determining the evolution of the stochastic processes under consideration. This paper examines the transient behaviour of relatively short transfer lines and derives the distribution of the performance measures of interest. An experiment is designed in order to compare the results of this study with the state-space representations and the simulation. Furthermore, extensions are briefly discussed and directions for future research are suggested.