Web services interact with each other over the Web to accomplish different business objectives, such interactions are known as services conversations, which are specified via the exchanged messages containing the operations to be invoked. Service consumers search the Web for services that fulfil their requirements. Unfortunately, due to services heterogeneities, services consumers usually cannot find the perfect match for their requests, hence they manually create adapters to mediate between chosen services and their requests. Creating such adapters manually becomes an obstacle for achieving high business agility, and definitely increases development efforts and costs. To overcome this problem, this paper proposes an approach for automatically generating conversations adapters. The proposed approach is ontology-based, where the adopted ontology provides the conversion semantics between application domain concepts via a graph data structure known as the concepts substitutability graph. The proposed approach uses such conversion semantics to determine the mappings between different conversation messages, and to generate the suitable concepts convertors, which are later used to build the required adapter. We believe the proposed approach helps in improving business agility and responsiveness, and of course minimizes efforts needed for developing SOA applications.