The paper discusses the consequences of anomalous Ward identities in quantum field theory, focusing on the SU(3) × SU(3) gauge group. It shows that anomalies must satisfy consistency or integrability relations, which restrict their possible form. Bardeen's anomalies for SU(3) × SU(3) are verified to satisfy these relations. A solution of the anomalous Ward identities is provided, which describes all anomalous contributions to low energy theorems. The paper also presents explicit expressions for anomalies in various processes, including strong five pseudoscalar interactions, K_{24}, and one- and two-photon interactions with three pseudoscalars. The anomalies are shown to depend on the structure of the gauge group, and the form of the minimal anomaly is determined up to an overall constant. The effective action, which satisfies the anomalous Ward identities, is model independent and describes anomalies in a model-independent way. The paper also notes that some expressions in the literature are incorrect because they do not account for the non-abelian structure of the group. The paper presents a local functional that satisfies the anomalous Ward identities and uses it to derive the effective Lagrangian for low energy consequences of anomalies. It provides explicit vertices for various processes, including the five pseudoscalar vertex, three pseudoscalar and one current vertex, and the two photon-three pion vertex. These vertices are derived from the effective action and are gauge invariant. The paper concludes that the anomalies are relevant to the physical world, as their predictions can be tested experimentally.The paper discusses the consequences of anomalous Ward identities in quantum field theory, focusing on the SU(3) × SU(3) gauge group. It shows that anomalies must satisfy consistency or integrability relations, which restrict their possible form. Bardeen's anomalies for SU(3) × SU(3) are verified to satisfy these relations. A solution of the anomalous Ward identities is provided, which describes all anomalous contributions to low energy theorems. The paper also presents explicit expressions for anomalies in various processes, including strong five pseudoscalar interactions, K_{24}, and one- and two-photon interactions with three pseudoscalars. The anomalies are shown to depend on the structure of the gauge group, and the form of the minimal anomaly is determined up to an overall constant. The effective action, which satisfies the anomalous Ward identities, is model independent and describes anomalies in a model-independent way. The paper also notes that some expressions in the literature are incorrect because they do not account for the non-abelian structure of the group. The paper presents a local functional that satisfies the anomalous Ward identities and uses it to derive the effective Lagrangian for low energy consequences of anomalies. It provides explicit vertices for various processes, including the five pseudoscalar vertex, three pseudoscalar and one current vertex, and the two photon-three pion vertex. These vertices are derived from the effective action and are gauge invariant. The paper concludes that the anomalies are relevant to the physical world, as their predictions can be tested experimentally.