This paper proposes a method in order to render passive discrete-time nonlinear multiple-input multiple-output (MIMO) systems which are affine in control. The methodology is based on the discrete-time version of the speed-gradient (SG) algorithm. For the application of the SG algorithm, quasi-V-passive and feedback quasi-V-passive systems are introduced. Two kinds of feedback laws rendering the system locally quasi-V-passive are obtained: a dynamic one and a static one. The feedback passivation methodology is applied to two examples. Some frequency-domain properties of the feedback transformed system are highlighted for the linear example. (c) 2007 Elsevier Ltd. All rights reserved.