  We study in detail the Hopf algebra of noncommutative symmetric functions in
superspace sNSym, introduced by Fishel, Lapointe and Pinto. We introduce a
family of primitive elements of sNSym and extend the noncommutative elementary
and power sum functions to superspace. Then, we give formulas relating these
families of functions. Also, we introduce noncommutative Ribbon Schur functions
in superspace and provide a explicit formula for their product. We show that
the dual basis of these function is given by a family of the so--called
fundamental quasisymmetric functions in superspace. This allows us to obtain a
explicit formula for the coproduct of fundamental quasisymmetric functions in
superspace. Additionally, by projecting the noncommutative Ribbon Schur
functions in superspace, we define a new basis for the algebra of symmetric
functions in superspace. On the other hand, we also show that sNSym can be
realised as a Hopf algebra of trees.
