In this Chapter, I introduce and illustrate a methodology for using a dialectical-relational version of CDA in transdisciplinary social research (Chouliaradi and Fairclough, 1999; Fairchough, 2003,2006). I begin with a theoretical section explaining the dialectical-relational approach, including my view of discourse, of critical analysis, and of transdisciplinary research. In the second section, I briefly discuss the fields of application of this approach, and in the third section, I explain the methodology, presenting it as a series of stages and steps, and identify a number of core analytical categories. In the fourth section, I present an example, showing the application of this methodology in researching a political topic, and illustrate the approach to political analysis in the fifth section with respect to particular texts. The sixth section summarizes what can be achieved with this methodology and discusses possible limitations.