In this study, a multi-mesh gear system subjected to torque fluctuations is employed as an example to study vibro-impacts of multi-degree-of-freedom systems having multiple clearances. Such rotational systems are common in various automotive geared drivetrains where external torque fluctuations lead to contact loss at gear mesh interfaces to result in sequences of impacts. The specific configuration considered here is a three-axis, two-gear mesh drivetrain that is commonly used in engine timing gear systems, known for its vibro-impacts resulting in rattling noise. On the theoretical side, a discrete torsion model is developed and solved using a piecewise-linear solution method. Its predictions are compared to measurements from a three-axis geartrain to demonstrate its accuracy. The validated model is exercised at the end to quantify sensitivity of vibro-impact motions and associated nonlinear behavior to key excitation parameters.