The Swedish curricula, as well as researchers and policy makers worldwide, have recognized the importance of promoting and including sociscientific argumentation in science education to promote scientific literacy. However, to teach socioscientific argumentation in not an easy task for science teachers and among the difficulties is the assessment practice. In this small-scale qualitative study, we have, investigated and compared how science and Swedish language teachers, participating in a SSI-driven project, assess students’ written argumentation about Global warming. The Swedish language teachers have a long tradition of teaching and assessing argumentation and therefore it is of interest to identify possible gaps between these two groups. The results indicate that the science teachers focus on students’ ability to reproduce content knowledge within their respective subject that they have been teaching. The Swedish language teachers include students’ abilities to select and use content knowledge from trustable reference resources, in addition to the structure of the argumentation and the form of the language used. In fact, the Swedish language teachers’ assessment correlates more to previous research about quality in socioscientific argumentation and we suggest that a closer co-operation between these two groups can be beneficial to enhance the quality of assessing students’ socioscientific argumentation.