This paper introduces Temporal Constraint Functional Programming (TCFP), a declarative paradigm suitable for concurrent programming. The paper defines an example TCFP language, a method for specifying the semantics of TCFP languages, and the basis of a transformation methodology for TCFP programs. The main advantages of TCFP are: Functional programs are free of control flow, allowing process bodies to be programmed without explicit reference to time or sequencing; Through temporal constraints, I/O, communication and time are explicitly recognized in a declarative way, and are formalized as a natural extension to the semantics of the underlying functional language; The temporal logic provides a natural abstraction for global and persistent state, long a problem in functional programming in the large; The framework gives support for transformation of concurrent programs, the correctness of which can be demonstrated via proofs in temporal logic.