This article deals with the special issue of Studie z aplikované lingvistiky / Studies in Applied Linguistics 1/2015 devoted to Critical Discourse Analysis, particularly one of its approaches, i.e. Discourse-Historical Approach (DHA). The studies included in the issue, i.e. Wodak and Reisigl’s model study explicating the main concepts and analytical tools of DHA and four case studies by Czech linguists inspired by DHA, are reanalyzed. Drawing on this reanalysis, the disputable aspects of the textual analysis conducted in the spirit of DHA are identified as follows: 1) the individual steps in the analysis (the identification of topics in the discourse analyzed, the identification of discursive strategies and the analysis of linguistic means) are implemented separately, hence the choice of linguistic expressions as a means of argumentation is not exposed and the discursive strategies of nomination and predication are analyzed separately; 2) the analysis shifts back and forth between the micro-context and the macro-context without adequate substantiation and does not devote sufficient attention to individual linguistic means; 3) the identification of topoi or fallacies does not sufficiently capture the role of linguistic means in argumentation and its relationship to other discursive strategies.