Transforming growth factor β (TGF-β) ligands activate a signaling cascade with multiple cell context dependent outcomes. Disruption or disturbance leads to variant clinical disorders. To develop strategies for disease intervention, delineation of the pathway in further detail is required. Current theoretical models of this pathway describe production and degradation of signal mediating proteins and signal transduction from the cell surface into the nucleus, whereas feedback loops have not exhaustively been included. In this study we present a mathematical model to determine the relevance of feedback regulators (Arkadia, Smad7, Smurf1, Smurf2, SnoN and Ski) on TGF-β target gene expression and the potential to initiate stable oscillations within a realistic parameter space. We employed massive sampling of the parameters space to pinpoint crucial players for potential oscillations as well as transcriptional product levels. We identified Smad7 and Smurf2 with the highest impact on the dynamics. Based on these findings, we conducted preliminary time course experiments.