The development of metaknowledge about models (MKM) and metaknowledge about the modelling process (MKP) are important in pre-service science teachers (PSTs) education. MKM refers to knowledge about the model's entities and its purposes, while MKP refers to knowledge about the components and structure of the modelling process. Assessing MKM and MKP is crucial to foster this knowledge in PSTs' education. However, assessment instruments focus on MKM rather than MKP, and the connection between MKM and MKP had not been examined deeply. This study validates and applies a diagram task for assessing PSTs' MKP. For validation, ten experts were surveyed and think-aloud interviews were conducted with ten PSTs. The findings support valid interpretations of PSTs' MKP based on the diagram task. In the main study, the diagram task was administrated to 63 PSTs, along with an MKM questionnaire. PSTs' MKP ranged from simple conceptions of modelling as a linear process including few components to sophisticated conceptions of modelling as an iterative process including multiple components. Furthermore, it was found that knowledge about using models to predict a phenomenon is an aspect connecting sophisticated MKM and MKP, indicating that this aspect is crucial to foster both, PSTs MKM and MKP.