A unit root testing procedure is presented that exploits the well-established power advantages of panel estimation while rectifying a deficiency in other panel unit root tests. This procedure, which takes into account contemporaneous cross-correlation and heterogeneous serial correlation of the regression residuals, allows determination of which members of the panel reject the null hypothesis of a unit root and which do not. Applying the procedure to real exchange rates yields results that are in broad agreement with those obtained from single-equation unit root tests. There is little evidence that a unit root can be rejected in dollar-based real exchange rates for the floating rate period.