Time series variables that stochastically trend together form a cointegrated system. In such systems, certain linear combinations of contemporaneous values of these variables have a lower order of integration than does each variable considered individually. These linear combinations are given by cointegrating vectors. OLS and NLS estimators of the parameters of a cointegrating vector are shown to converge in probability to their true values at the rate T^1^-^@d for any positive @d. These estimators can be written asymptotically in terms of relatively simple nonnormal random matrices which do not depend on the parameters of the system. These asymptotic representations form the basis for simple and fast Monte Carlo calculations of the limiting distributions of these estimators. Asymptotic distributions thus computed are tabulated for several cointegrated processes.