This paper considers cointegration tests for dynamic systems where the number of variables is large relative to the sample size. Typical examples include tests for unit roots in panels, where the units are linked by complicated dynamic relationships. It is well known that conventional cointegration tests based on a parametric (vector autoregressive) representation of the system break down if the number of variables approaches the number of time periods. To sidestep this difficulty we propose nonparametric cointegration tests based on eigenvalue problems that are asymptotically free of nuisance parameters. Furthermore, a nonparametric panel unit root test is suggested. It turns out that if the number of variables is large, the nonparametric tests outperform their parametric (likelihood-ratio based) counterparts by a clear margin.