Self-organization of nonlinear waves underpins phenomena ranging from hydrodynamic pattern formation to optical frequency-comb generation. We introduce and numerically demonstrate a shift-register synchronization mechanism for pulse trains in quadratic nonlinear resonators. The synchronized state persists despite substantial group-velocity mismatch through continuous parametric energy exchange, resulting in deterministic discrete pulse shifts after each cavity round trip. Nonlinear parametric interaction modifies the effective walk-off, allowing the pulse trains to satisfy the shift-register synchronization conditions. The proposed mechanism reveals a previously unexplored synchronization regime in quadratic resonators and provides a route toward multicolour frequency combs, optical memories, and ultrafast photonic information processing.