Epidermal growth factor receptor (EGFR)-mediated signal transduction is often hyperactivated in tumour cells and therefore considered a promising target for cancer therapy. A number of computational models have been developed which describe the pathway in great detail. These models are similar in their description of the activation events. The deactivation of the EGFR signalling seems to be cell type-specific and is less understood. Deactivation via receptor internalization, feedback inhibition of son of sevenless (SOS) by double phosphorylated, extracellular signal-regulated kinase (ERKPP) or transiently activated Ras-GTPase activating protein (Ras-GAP) proteins is discussed to play a role. In this study we address the question of to what extent the effect of oncogenic perturbations on EGFR signalling depend on the specific regulation structure. This is investigated using a detailed pathway model under two regulatory modes: the negative feedback via ERKPP to SOS and feed-forward deactivation via transiently activated Ras-GAP proteins. We show that the effect of receptor overexpression differs qualitatively under both regulations. In the system with transiently activated Ras-GAP it may result in an attenuation of the ERK activation. Such a nonintuitive effect was also observed experimentally. In general we find the model with transiently activated Ras-GAP to have a higher robustness towards receptor overexpression and Ras mutations. In particular, we demonstrate that this model can compensate for these oncogenic perturbations if the regulation is strong. The negative feedback can not protect the system against Ras mutations. A general sensitivity analysis, however, shows a higher robustness of the model under negative feedback, indicating the limited significance of such analyses for the prediction of specific oncogenic perturbations.