Maude 2.0 is the new version of the Maude rewriting logic language currently under development. Maude 2.0's three main goals are: (i) greater generality and expressiveness; (ii) efficient support for a wider range of programming applications; and (iii) usability as a key component for developing internet programming and mobile computing systems. To meet these goals, a number of new features have been added. The membership equational logic of functional modules and the rewriting logic of system modules are now supported in their greatest possible generality, and the operational semantics of object-oriented modules guarantees object and message fairness. Module operations in Full Maude are also more general thanks to parameterized theories and views. Efficient support for a wider range of programming applications is provided both by the Maude compiler—which can reach up to 15 million rewrites per second on a 667MHz Xeon—and by a library of new built-in modules. Besides new built-in functional modules, a key new feature is built-in object-oriented modules that provide flexible interaction with external objects such as file systems, window systems, and internet sockets. In particular, built-in internet sockets will provide excellent support for a new declarative style of internet programming in Maude, and will be used as a key building block to implement the Mobile Maude language.