This article proposes a general modelling approach for locomotion dynamics of Mobile Multibody Systems (MMS) containing passive internal degrees of freedom (dofs) concentrated into (ideal or not) joints and/or distributed along deformable bodies of the system. The approach embraces the case of non-holonomic mobile multibody systems with passive wheels, the pendular climbers and the locomotion systems bio-inspired by animals that exploit the advantages of soft appendages such as the fish

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... with their caudal fin or the moths using the softness of their flapping wings to improve flight performance. The article proposes a general structured modelling approach of MMS with tree-like structures along with efficient computational algorithms of the resulting equations. The approach is illustrated through non-trivial examples such as the 3D bicycle and a compliant version of the snake-board.