We present experiments with automatic annotation of English texts, taken from the Penn Treebank, at the dependency-based tectogrammatical layer, as it is defined in the Prague Dependency Treebank. The proposed analyzer, which is based on machine-learning techniques, outperforms a tool based on hand-written rules, which is used for partial tectogrammatical annotation of English now, in the most important characteristics of tectogrammatical annotation. Moreover, both tools were combined and their combination gives the best results.