© 2019, Emerald Publishing Limited. Purpose: The purpose of this paper is to explore the conversation activities of design teams to negotiate task conflict and reach consensus. Design/methodology/approach: Four case studies were conducted to analyse the conversation activities that teams use in the course of design projects. Findings: The conversation activities that teams used to negotiate conflict and bring about consensus were identified. These conversation activities are associated with collaboration, communication and social skills enabling teams to engage in the high level of information exchange and negotiation that is required to manage task conflict. How they were used to negotiate conflict and help reach consensus is also discussed. Research limitations/implications: The findings from this research are based on a small number of participants; hence, it cannot be generalised without further study with larger groups. However, the questions this paper has raised can be generalised to other design tasks and groups. Practical implications: The findings have implications for the management of design teams and teams working on complex unstructured problems both in industry and education. They highlight how conflict can be constructively managed to bring about consensus that integrates the knowledge and perspective of all team members. Originality/value: The benefits of task conflict have been disputed in the literature. This research has identified the conversation activities that facilitate the constructive management of task conflict to bring about consensus that integrates the perspectives and knowledge of a team.