The paper deals with the models for pipelines in transient mode. The nonlinear distributed parameter model is first linearized and a two input - two output system is obtained. The models represented by basic canonical equations are then rearranged into four feed-back models (two hybrid, impedance and admittance) which are capable to describe the oscillations phenomena. Transfer functions in the feed-back models are transcendent with a time delay. Transcendent transfer functions are then approximated with rational transfer functions. The derived models are validated on a real pipeline data during start-up and shutdown phase of the operation.