  In this work, first, we study a flat Friedmann-Robertson-Walker Universe with
two scalar fields but only one potential term, which can be thought as a simple
quintessence plus a K-essence model. Employing the Hamiltonian formalism we are
able to obtain the classical and quantum solutions. The second model studied,
is also a flat Friedmann-Robertson-Walker Universe with two scalar fields, with
the difference that the two potentials are considered as well as the standard
kinetic energy and the mixed term (chiral field approach). Regarding this
second model, it is shown that setting to zero the coefficient accompanying the
mixed momenta term, two possible cases can be studied: a quintom like case
($m^{12}_{+}$) and a quintessence like case ($m^{12}_{-}$). For both scenarios
classical and quantum solutions are presented.
