Antiferromagnets and ferrimagnets are two kinds of classic magnetic materials and are particularly important for modern magnonic and spintronic devices because of their steadily coupled antiferromagnetic sublattices, which result in chirality-dependent magnons, efficient charge-spin conversion, altermagnetism, and great scalability for high-density integration. However, here, we report the observation of asynchrony among sublattices by using typical CoGd ferrimagnets, where the antiferromagnetically coupled sublattices fail to remain synchronized during high-speed precession. By employing magnetic resonance, we demonstrate that the asynchrony occurs when the resonance frequency exceeds a critical value corresponding to the delay time (τd) between the two sublattices under microwave excitations. The determined τd is about 60 ps in CoGd, varies slightly with temperature and composition, but decreases sharply near magnetization and angular momentum compensation. These results demonstrate the speed limit of device performance relying on the antiferromagnetically coupled sublattices as a matter of fundamental principle, and also indicate that the antiferromagnetic attributes during high-speed operations cannot be described as statically coupled sublattices.