Design-oriented research practices create opportunities to construct knowledge that is more abstracted than particular instances, without aspiring to be at the scope of generalized theories. We propose an intermediate design knowledge form that we name strong concepts with the following properties: generative, carries a core design idea, cuts across particular use situations and even application domains; concerns interactive behaviour, not static appearance; is a design element, a part of an artefact, and at the same time speaks of a use practice and behaviour over time; and finally, residing on an abstraction level above particular instances. We exemplify with two strong concepts: social navigation and seamfulness, and discuss how these fulfil criteria we might have on knowledge, such as being contestable, defensible and substantive. Our aim is to foster an academic culture of discursive knowledge construction of intermediate-level knowledge and how it can be produced and assessed in design-oriented HCI research.