  We present, for the first time, the complete off-shell $4D, {\cal N}=2$
superfield actions for any free massless integer spin ${\bf s} \geq 2$ fields,
using the ${\cal N}=2$ harmonic superspace approach. The relevant gauge
supermultiplet is accommodated by two real analytic bosonic superfields
$h^{++}_{\alpha(s-1)\dot\alpha(s-1)}$, $h^{++}_{\alpha(s-2)\dot\alpha(s-2)}$
and two conjugated complex analytic spinor superfields
$h^{+3}_{\alpha(s-1)\dot\alpha(s-2)}$, $h^{+3}_{\alpha(s-2)\dot\alpha(s-1)}\,$,
where $\alpha(s) := (\alpha_1\ldots \alpha_s), \dot\alpha(s) :=
(\dot\alpha_1\ldots \dot\alpha_s)$. Like in the harmonic superspace
formulations of ${\cal N}=2$ Maxwell and supergravity theories, an infinite
number of original off-shell degrees of freedom is reduced to the finite set
(in WZ-type gauge) due to an infinite number of the component gauge parameters
in the analytic superfield parameters. On shell, the standard spin content
$({\bf s, s-1/2, s-1/2, s-1})$ is restored. For ${\bf s}=2$ the action
describes the linearized version of "minimal" ${\cal N}=2$ Einstein
supergravity.
