Engle-Granger and ECM with trend stationary series

[depres]

Earlier I have made analysis only with difference stationary series, but now all needed variables are trend stationary ones. The aim is to get a error correction model by using Engle-Granger two step procedure, but now I am not sure which form of variables I should use in different steps of analysis. With difference stationary variables it is clear: realizing first step (OLS-regression, LR-relations) with logarithmic forms, saving the residual of that regression and making ECM with differenced logarithmic form of variables. But how to do with trendstationary ones ?

Is it OK, if I use logarithmic forms of trend stationary variables in the first step (OLS-regression), save the residual of that model, de-trend logarithmic forms after it, take differences of those de-trended forms and use those differences in EC-modelling ? Or error correction model with de-trended logarithmic forms without differencing at all?

Thanks for help in advance already !