Neocortical feedback is critical for attention, prediction, and learning. To mechanically understand its function requires deciphering its cell-type wiring. Recent studies revealed that feedback between primary motor to primary somatosensory areas in mice is disinhibitory, targeting vasoactive intestinal peptide-expressing interneurons, in addition to pyramidal cells. It is unknown whether this circuit motif represents a general cortico-cortical feedback organizing principle. Here we show that in contrast to this wiring rule, feedback between higher-order lateromedial visual area to primary visual cortex preferentially activates somatostatin-expressing interneurons. Functionally, both feedback circuits temporally sharpen feed-forward excitation eliciting a transient increase-followed by a prolonged decrease-in pyramidal cell activity under sustained feed-forward input. However, under feed-forward transient input, the primary motor to primary somatosensory cortex feedback facilitates bursting while lateromedial area to primary visual cortex feedback increases time precision. Our findings argue for multiple cortico-cortical feedback motifs implementing different dynamic non-linear operations.