Abstract Mergers of black holes (BHs) and neutron stars (NSs) result in the emission of gravitational waves that can be detected by LIGO. In this paper, we look at 2+2 and 3+1 quadruple-star systems, which are common among massive stars, the progenitors of BHs and NSs. We carry out a detailed population synthesis of quadruple systems using the Multiple Stellar Evolution code, which seamlessly takes into consideration stellar evolution, binary and tertiary interactions, N-body dynamics, and secular evolution. We find that, although secular evolution plays a role in compact object (BH and NS) mergers, (70–85)% (depending on the model assumptions) of the mergers are solely due to common envelope evolution. Significant eccentricities in the LIGO band (higher than 0.01) are only obtained with zero supernova (SN) kicks and are directly linked to the role of secular evolution. A similar outlier effect is seen in the χ _eff distribution, with negative values obtained only with zero SN kicks. When kicks are taken into account, there are no systems that evolve into a quadruple consisting of four compact objects. For our fiducial model, we estimate the merger rates (in units of Gpc⁻³ yr⁻¹) in 2+2 quadruples (3+1 quadruples) to be 10.8 ± 0.9 (2.9 ± 0.5), 5.7 ± 0.6 (1.4 ± 0.4), and 0.6 ± 0.2 (0.7 ± 0.3) for BH–BH, BH–NS, and NS–NS mergers, respectively. The BH–BH merger rates represent a significant fraction of the current LIGO rates, whereas the other merger rates fall short of LIGO estimates.