We establish relations between seismic scaling parameters for general distributions of subevents in a composite (multiple event) model of faulting. The radiation from the main seismic event is presumed to be produced by a multitude of smaller earthquakes (subevents) with a range of source sizes. Under the composite earthquake hypothesis, the seismic moment scaling—the dependence of the seismic moment on the event's size—is the same for the large earthquake and all its components. If at lowest frequencies the subevent spectra add coherently, and at higher frequencies (above the corner frequency of the smallest subevent) the spectra add incoherently, then γ = δ/2 and α > 1, where γ is the high-frequency spectral fall-off, δ determines the scaling of seismic moment M0 with source size R (such that M0R−° is constant), and α is the fraction of the total rupture area occupied by subevents. In each particular case, these relations can be used to verify whether the studied large earthquake is a composite of smaller earthquakes.