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The interactions between inputs and outputs in the multi input multi output (MIMO) systems yield responses from closed-loop off-diagonal elements. To characterize these responses through modeling, a systematic approach is followed to derive analytical expressions for relay feedback responses on multivariable systems. Time domain analytical expressions are helpful in deriving boundary conditions to estimate the parameters of MIMO systems. Unknown system parameters are identified using limit cycle data of off-diagonal closed-loop relay response curves obtained from single relay feedback test on these MIMO systems. Developed models are found to be in close agreement with real time system, and the parametric identification procedure is also efficient. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1672-1681, 2014 [ABSTRACT FROM AUTHOR]