The adaptive relay, control of single-input second-order systems is considered. The plant parameters are assumed constant, but unknown. The controller dispenses with a learning (or identification) phase and does not organize itself through adaptive correction, but identifies a certain curve in the state space. This curve is associated with sliding motion. The strategy is analysed for the double-integrator plant. The identical controller can be applied to other second-order plants. The system response is found to be close to the time-optimal response.