The Kuramoto model is a paradigmatic model of coupled phase-oscillators. Each oscillator has the natural frequency, obeying a probability distribution function, and couples with the other oscillators through the sinusoidal coupling function. The Kuramoto model exhibits the synchronization transition, from the nonsynchronized state to the synchronized state, and the critical exponents characterize the transition. Daido calculated in the Kuramoto model the critical exponents defined by applying an external force when the natural frequencies obey the Lorentz distribution . How- ever, the existence and the classification of the universality classes is unknown, while the universality classes are established in statistical mechanics. In this talk, we discuss two types of universality. First, we investigate the critical exponents in the Kuramoto model for two families of natural frequency distributions, including the Lorentz distribution or the Gaussian distribution. Second, we discuss the critical exponents when we add a second mode to the coupling function.
 H. Daido, Susceptibility of large populations of coupled oscillators, Phys. Rev. E 91, 012925 (2015).