We present a set of adaptive methods and rules for routing messages in an EAI infrastructure that yields a form of autonomic behavior, namely the ability to dynamically optimize the flow of messages in order to respect SLA according to business priorities. EAI (Enterprise Application Integration) infrastructures may be seen as component systems that exchange asynchronous messages over an application bus, under the supervision of a processflow engine that orchestrates the messages. The QoS (Quality of Service) of the global IT system is defined and monitored with SLA (Service Level Agreements) that apply to each business process. The goal of this paper is to propose routing strategies for message handling that maximize the ability of the EAI system to meet these requirements, in a self-adaptive and self-healing manner, which is the ability to cope with sudden variations of the event flow or temporary failures of a component system.