The spin structure of amplitudes for the production of a single baryon or meson resonance of arbitrary spin in a quasi-two-body final state has been investigated. If the dominant mechanism is the exchange of a single set of quantum numbers in the crossed channel, the spin density matrix elements are shown to satisfy bilinear relations. Typical relations are (Reρm,n)2+(Reρm,- n)2=ρmmρnn for baryon production, and (Reρm,n+/-Reρm,- n)2=(ρmm+/-ρm,-m) (ρnn+/-ρn,-n) for meson production. It is suggested that the use of these relations in the analysis of data is a good test for the presence of two or more exchange contributions. The relations are used to analyze vector- and tensor-meson production from πN and KN initial states, and ∆(1236) production from πN and NN initial states. Two of the most interesting results concern ∆ production. We find that the small-angle data on NN-->N∆ cannot be dominated by π exchange alone, and analysis of the data on πN-->π∆ at 8 GeVc indicates the existence of contributions in addition to ρ exchange.