Epithelial-mesenchymal transition (EMT) is a key event in the generation of invasive tumor cells. A hallmark of EMT is the repression of E-cadherin expression, which is regulated by various signal transduction pathways including extracellular signal-regulated kinase (ERK) and Wnt. These pathways are highly interconnected via multiple coupled feedback loops (CFL). As the function of such coupled feedback regulations is difficult to analyze experimentally, we used a systems biology approach where computational models were designed to predict biological effects that result from the complex interplay of CFLs. Using epidermal growth factor (EGF) and Wnt as input and E-cadherin transcriptional regulation as output, we established an ordinary differential equation model of the ERK and Wnt signaling network containing six feedback links and used extensive computer simulations to analyze the effects of these feedback links in isolation and different combinations. The results show that the feedbacks can generate a rich dynamic behavior leading to various dose-response patterns and have a decisive role in determining network responses to EGF and Wnt. In particular, we made two important findings: first, that coupled positive feedback loops composed of phosphorylation of Raf kinase inhibitor RKIP by ERK and transcriptional repression of RKIP by Snail have an essential role in causing a switch-like behavior of E-cadherin expression; and second, that RKIP expression inhibits EMT progression by preventing E-cadherin suppression. Taken together, our findings provide us with a system-level understanding of how RKIP can regulate EMT progression and may explain why RKIP is downregulated in so many metastatic cancer cells.