Pointwise consistent, feasible procedures for estimating contemporaneous linear causal structure from time series data have been developed using multiple conditional independence tests, but no such procedures are available for non-linear systems. We describe a feasible procedure for learning a class of non-linear time series structures, which we call additive non-linear time series. We show that for data generated from stationary models of this type, two classes of conditional independence relations among time series variables and their lags can be tested efficiently and consistently using tests based on additive model regression. Combining results of statistical tests for these two classes of conditional independence relations and the temporal structure of time series data, a new consistent model specification procedure is able to extract relatively detailed causal information. We investigate the finite sample behavior of the procedure through simulation, and illustrate the application of this method through analysis of the possible causal connections among four ocean indices. Several variants of the procedure are also discussed.