Software in Ubiquitous Computing is faced with a dynamic and heterogeneous environment. For tapping the environment's full potential, software must be able to adapt dynamically and react to the environment in a platform-and language-independent manner. However, developing mobile and adaptive applications is a complex and error-prone task. This work presents the design of SAMProc, a new middleware that supports developers in creating ubiquitous applications. We introduce the novel concept of self-adaptive mobile processes, which allows an abstract high-level specification of an application's lifecycle and its distribution aspects. In our system, an application may dynamically migrate with an adaptation of its interface, state and implementation at runtime, while transparently and permanently remaining addressable. The SAMProc middleware uses an MDA-like approach, in which the developer creates a self-adaptive mobile process description. A middleware tool automatically maps these descriptions to our infrastructure, i.e., either self-adaptive migratable CORBA objects or Web services. The developer focuses on application logic; the tool generates migration and adaptation code. We demonstrate the feasibility by presenting an example application in which mobile reporters publish data in a basic workflow.