This paper examines electronic instruments that are based on dynamical systems, where the behaviour of the instrument depends not only upon the immediate input to the instrument, but also on the past input. Five instruments are presented as case studies: Michel Waisvisz’ Cracklebox, Dylan Menzies’ Spiro, no-input mixing desk, the author’s Feedback Joypad, and microphone-loudspeaker feedback. Links are suggested between the sonic affordances of each instrument and the dynamical mechanisms embedded in them. This is discussed in the context of contemporary, materialoriented approaches to composition and particularly to free improvisation where elements such as unpredictability and instability are often of interest, and the process of exploration and discovery is an important part of the practice. Links are also made with the use of dynamical interactions in computer games to produce situations in which slight variations in the timing and ordering of inputs can lead to very different outcomes, encouraging similarly explorative approaches.