  In this paper we consider dimonoids, which are sets equipped with two
associative binary operations. Dimonoids in the sense of J.-L. Loday are
xamples of duplexes. The set of all permutations, gives an example of a duplex
which is not a dimonoid. We construct a free duplex generated by a given set
via planar trees and then we prove that the set of all permutations form a free
duplex on an explicitly described set of generators. We also consider duplexes
coming from planar binary trees and vertices of the cubes. We prove that these
duplexes are free with one generator in appropriate variety of duplexes.
