  A ${\mathbb{Z}}_2{\mathbb{Z}}_4$-additive code ${\cal
C}\subseteq{\mathbb{Z}}_2^\alpha\times{\mathbb{Z}}_4^\beta$ is called cyclic if
the set of coordinates can be partitioned into two subsets, the set of
${\mathbb{Z}}_2$ and the set of ${\mathbb{Z}}_4$ coordinates, such that any
cyclic shift of the coordinates of both subsets leaves the code invariant.
These codes can be identified as submodules of the $\mathbb{Z}_4[x]$-module
$\mathbb{Z}_2[x]/(x^\alpha-1)\times\mathbb{Z}_4[x]/(x^\beta-1)$. The parameters
of a ${\mathbb{Z}}_2{\mathbb{Z}}_4$-additive cyclic code are stated in terms of
the degrees of the generator polynomials of the code. The generator polynomials
of the dual code of a ${\mathbb{Z}}_2{\mathbb{Z}}_4$-additive cyclic code are
determined in terms of the generator polynomials of the code ${\cal C}$.
