Various types of magnetic resonance signals observed in quantum-disordered magnets of the Haldane and dimer types are reported. The collective states of correlated spins near the breaks of the S=1 spin chains in the Haldane magnet PbNi2V2O8 demonstrate magnetic response of an effective spin S=1/2, while the excited states of long chains reveal the ESR spectrum of an effective spin S=1 in a crystal field. A magnetic resonance spectrum of the latter type is also observed for the collective excited states in the system of coupled S=12 dimers in crystals of TlCuCl3. Further, the interaction of triplet excitations and defects in PbNi2V2O8 is shown to result in a hybrid spin resonance mode.