We present a search for the pair production of a narrow nonstandard-model strongly interacting particle that decays to a pair of quarks or gluons, leading to a final state with four hadronic jets. We consider both nonresonant production via an intermediate gluon as well as resonant production via a distinct nonstandard-model intermediate strongly interacting particle. We use data collected by the CDF experiment in proton-antiproton collisions at s√=1.96 TeV corresponding to an integrated luminosity of 6.6 fb−1. We find the data to be consistent with nonresonant production. We report limits on σ(pp¯→jjjj) as a function of the masses of the hypothetical intermediate particles. Upper limits on the production cross sections for nonstandard-model particles in several resonant and nonresonant processes are also derived.