The Web Services Resource Framework (WSRF) has redefined grid computing standards, making Web services more suitable for grid applications by adding persistent state management. However, it is still difficult to build, deploy, and evolve such services, since different Web and grid services containers require that the services they host be written in specific languages, to target particular internal interfaces for state management. Therefore, services must be built and deployed differently for each hosting environment. This paper describes uniform dynamic service code deployment on three Web services containers (namely, Tomcat, ASP.NET and a gSOAP based C++ container), and two grid services containers (namely, GT4 and WSRF.NET). Containers receive the code in an XML-based standard intermediate form, and then generate container-specific native code in different languages, without exposing these details to applications and grid services programmers. The dynamically deployed code can access state managed by the hosting container, can utilize functionalities exposed by statically deployed services, and can communicate with other dynamically deployed modules, running either in the same container or in different containers. A performance study shows that the newly deployed mobile code can run nearly as efficiently as it would if it had been deployed statically, through container-specific mechanisms.