The concurrent synchronous language Esterel allows programmers to treat reactive systems in an abstract, concise manner. An Esterel program is typically first translated into other, non-synchronous high-level languages, such as VHDL or C, and then compiled further into hardware or software. Another approach that has been proposed recently is the direct execution of Esterel-like instructions with a customized processor, which promises the flexibility of a software solution with an efficiency close to a hardware implementation. However, the instruction sets and implementations of the processor architectures proposed so far still have some limitations regarding their completeness, efficiency, and adherence to the original Esterel semantics. This paper presents a novel reactive processor architecture, the Kiel Esterel Processor, which addresses these shortcomings. In particular, it provides a complete, semantically accurate implementation of the Esterel preemption primitives, most of which can be expressed directly with a single machine instruction. One advantage of the reactive processors-in addition to their high execution speed compared to traditional software implementations-is that control-flow is preserved while compiling Esterel into machine code, and that the execution platform has a very predictable timing behavior. This paper presents a precise and very efficient Worst Case Reaction Time (WCRT) analysis, which is geared towards the Kiel Esterel Processor, but which could be adapted to other reactive processors as well.