Autotuning by relay feedback is studied with emphasis on multiloop PID control of two-input two-output systems. For the purpose of control design many chemical engineering processes can be modeled by integrator-plus-dead-time or gain-plus-dead-time models. Relay feedback is a convenient method to identify the model parameters, the form of the output response indicating which model is preferable. For a multi-input multi-output process, the off-diagonal elements can be determined in the same experiment as the diagonal elements. The usefulness of the approach is illustrated by a number of systems, including processes with inverse response. Two experimental two-input two-output processes, a mixing tank and a distillation column are used, both with and without decoupling. The approach results in decouplers of simple forms. Autotuning is useful also for tuning the decoupled system.