We derive a time-domain mean-field equation to model the full temporal and spectral dynamics of light in singly resonant cavity-enhanced second-harmonic generation systems. We show that the temporal walkoff between the fundamental and the second-harmonic fields plays a decisive role under realistic conditions, giving rise to rich, previously unidentified nonlinear behavior. Through linear stability analysis and numerical simulations, we discover a new kind of quadratic modulation instability which leads to the formation of optical frequency combs and associated time-domain dissipative structures. Our numerical simulations show excellent agreement with recent experimental observations of frequency combs in quadratic nonlinear media [Phys. Rev. A 91, 063839 (2015)]. Thus, in addition to unveiling a new, experimentally accessible regime of nonlinear dynamics, our work enables predictive modeling of frequency comb generation in cavity-enhanced second-harmonic generation systems. We expect our findings to have wide impact on the study of temporal and spectral dynamics in a diverse range of dispersive, quadratically nonlinear resonators. DOI: 10.1103/PhysRevLett.116.033901 The generation of frequency combs in high-Q microresonators has attracted significant attention over the last decade [1]. These combs originate from the third-order optical (Kerr) nonlinearity [2]: four-wave mixing drives modulation instability (MI), leading to the growth of signal and idler sidebands [3]. In the time domain, such "Kerr" combs can correspond to temporal dissipative patterns or localised structures-temporal cavity solitons [4][5][6].Certain microresonators exhibit a weak second-order χnonlinearity, which may lead to the intracavity conversion of the Kerr comb to shorter wavelengths [7,8]. But recent experiments in free-space resonators have remarkably demonstrated that frequency combs can also arise entirely through χ ð2Þ effects. On the one hand, it is known that cascaded second-harmonic generation (SHG), subject to large phase mismatch, can give rise to an effective Kerr nonlinearity [9,10], and comb generation has indeed been observed under such conditions [11,12]. But on the other hand, frequency combs have recently been observed also for phase-matched cavity-enhanced SHG [13].In cavity-enhanced SHG, comb formation initiates from the spontaneous down-conversion of the second-harmonic field [13], a process widely investigated in the context of internally pumped optical parametric oscillators (OPOs) [14][15][16][17]. However, theoretical analyses have hitherto been limited to a very small number of frequency components: no models have been put forward that would allow for the full frequency comb dynamics to be examined. For quadratically nonlinear, spatially diffractive cavities, full models do exist, and their study has revealed numerous spatial phenomena whose temporal analogs would be associated with frequency combs, including pattern formation [17][18][19] and quadratic cavity solitons [20]. Unfortunately, insights obtained ...