We study a class of generalized self-duality relations in gauge theories on the complex projective space with the Fubini–Study metric. Our theories consist of only gauge fields with gauge group U(n). The pseudoenergies which we consider contain higher orders of field strength and are labeled by an integer p smaller than or equal to [n/2]. For making the Bogomol’nyi completion we need nonsingle trace terms in the pseudoenergies, unlike the models defined on spheres, which were studied previously. We construct an explicit solution in dimension 2n to generalized self-duality equations as Bogomol’nyi equations by using a part of the spin connection.