Needless to say, distributed algorithms are usually hard to design mush harder to prove and to use in real distributed systems. In these systems, local computations theory has proved its power to formalize and prove in an intuitive way distributed algorithms. This paper uses this formalism to present solutions to the election problem in several network topologies using mobile agents at the design and the implementation levels. We formalized the proposed solutions in the local computations model using transition systems [11]. This facilitates the proof of the proposed solutions using the mathematical tool-box provided by the local computation theory. Using mobile agents, the proposed solutions get rid of synchronization and do not need continuous use of all machines computational resources. Proposed solutions are also simulated within the VISIDIA [3] platform.