Transdisciplinary research (TDR) is increasingly promoted in current science policy. It is expected to address complex societal issues while both being democratically just and challenging deep-seated epistemological assumptions. The rising emphasis on accountability and evaluation in science has led to a growing literature on TDR evaluation over the last 15 years. Existing reviews of this literature often aim to synthesize results into general overarching evaluation frameworks. However, these reviews have paid limited attention to the normative assumptions embedded within evaluation criteria. This risks smoothing over deep-seated conflicts regarding values and goals in TDR. In this paper, we qualitatively analyse a systematically identified corpus of 58 peer-reviewed articles to uncover the underlying normative assumptions that are prominent in the TDR evaluation literature. We identify four distinct discourses: Justification, providing explanation and motivation for TDR; Integration, focusing on the epistemological dimension of TDR; Impact, aiming to better understand how TDR leads to societal effects; and Metrics, indicators of TDR effects. We argue that the dominance of the Impact discourse risks overlooking the epistemological ambitions of TDR, while the consensus-oriented Integration discourse risks smoothing over pluralism and minimizing heterodox views among participants. Both funders and evaluators of TDR must be aware of and reflect on the implications of their normative assumptions for the specific contexts in which they operate. Our results can serve as a conceptual tool that helps navigate the complexities and assumptions of TDR evaluation.