  The two-phase horizontally periodic quasistationary Stokes flow in
$\mathbb{R}^2$, describing the motion of two immiscible fluids with equal
viscosities that are separated by a sharp interface, which is parameterized as
the graph of a function $f=f(t)$, is considered in the general case when both
gravity and surface tension effects are included. Using potential theory, the
moving boundary problem is formulated as a fully nonlinear and nonlocal
parabolic problem for the function $f$. Based on abstract parabolic theory, it
is proven that the problem is well-posed in all subcritical spaces
$\mathrm{H}^r(\mathbb{S})$, $r\in(3/2,2)$. Moreover, the stability properties
of the flat equilibria are analyzed in dependence on the physical properties of
the fluids.
