The liquidity problems that appeared on the interbank money markets during the financial crisis caused an increased volatility of the interbank interest rates, especially after September 2008. Banking institutions from the Euro zone have avoided the mutual funding, which resulted in a reduction of the interbank interest rates due to the excess liquidity on the interbank money markets. In these conditions we want to analyze the behavior of interbank interest rates for several CEE transition countries, responding to the following question: will they return to the long run equilibrium or will they follow a random walk? In our research we deal with unit root tests taking into consideration structural breaks and the persistence of the volatility. We also examine the long run equilibrium between the term structures of interest rates appealing at the cointegration analysis and proposing some Vector Autoregressive models. Finally, we asses the cointegration between the interbank money markets from Euro zone, Bulgaria, Czech Republic, Hungary, Poland and Romania and propose some volatility transmission models