Multisite phosphorylation cycles are ubiquitous in cell regulation and are studied at multiple levels of complexity, with the ultimate goal to establish a quantitative view of phosphorylation networks in vivo. Achieving this goal is essentially impossible without mathematical models. Several models of multisite phosphorylation have been already proposed in the literature and received considerable attention from both experimentalists and theorists. Most of these models do not discriminate between distinct partially phosphorylated states of the regulated proteins and focus on two limiting regimes, distributive and processive, which differ in the number of enzyme substrate encounters needed for complete phosphorylation or dephosphorylation. Here we use the minimal model of ERK regulation to explore the dynamics of multisite phosphorylation in a reaction network that includes all essential phosphorylation states and varying levels of reaction processivity. In addition to bistability, which has been extensively studied in models with distributive mechanisms, this network can also generate oscillations, in which the relative abundances of the four phosphorylation states change in an ordered way. Both bistability and oscillations are suppressed at high levels of reaction processivity. Our work provides a general approach for large scale analysis of dynamics in multisite phosphorylation systems.