A vector autoregressive model allowing for unit roots as well as an explosive characteristic root is developed. The Granger-Johansen representation shows that this results in processes with two common features: a random walk and an explosively growing process. Cointegrating and coexplosive vector… s can be found that eliminate these common factors. The likelihood ratio test for a simple hypothesis on the coexplosive vectors is analyzed. The method is illustrated using data from the extreme Yugoslavian hyperinflation of the 1990s.