In this paper we study the determinants of international migration to Germany, 1967-2000. The empirical literature on macro-economic migration functions usually explains migration flows by a set of explanatory variables such as the income differential, employment rates, and migrations stocks as in Hatton (1995), for example. Since macroeconomic variables are widely acknowledged as nonstationary, the standard model in the migration literature can only meet the requirements of modern non-stationary time-series econometrics if migrations flows and the explanatory variables are integrated of the same order and if these variables form a cointegrated set. In order to prove whether the standard specification is compatible with our data, we use the univariate Augmented Dickey-Fuller test as well as its panel data version, developed in Im, Pesaran, and Shin (2003), to test for unit roots in the time series. The tests demonstrate that migration rates are stationary, while the remaining explanatory variables follow I(1) processes. Consequently, we suggest an alternative specification of the long-run migration function with migration stocks as the dependent variable. For this specification, we find that all variables are I(1) processes, and that the null of no cointegration can be decisively rejected by applying the panel cointegration test of Pedroni (1999). The parameter inference in the cointegrating regressions is conducted using the method of canonical cointegrating regressions of Park (1992). Our empirical findings generally agree with predictions of migration theory.