Co-quasiorder relations, the constructive counterpart of classical quasiorder relations are examined within the framework of Bishop’s constructive mathematics. Two classically equivalent, but constructively inequivalent, notions of co-quasorder are investigated. It turns out that a weak co-quasorder is a co-quasiorder if and only if it is quasi-detachable. As a consequence, the incomparability relation associated to a co-quasiorder is quasi-detachable.