  Gizatullin surfaces of type $[[0,0,-r_2,-r_3]]$ can be described by the
equations $yu = x P(x)$, $xv = u Q(u)$ and $yv = P(x) Q(u)$ in
$\mathbb{C}^4_{x,y,u,v}$ where $P$ and $Q$ are non-constant polynomials. We
establish the algebraic density property for smooth Gizatullin surfaces of this
type. Moreover we also prove the density property for smooth surfaces given by
these equations when $P$ and $Q$ are holomorphic functions.
