  We analyze a pion form factor formulation which fulfills the Analyticity
requirement within the Hidden Local Symmetry (HLS) Model. We show that it
implies an $s$--dependent dressing of the $\rho-\gamma$ VMD coupling and an
account of several coupled channels. The corresponding function $F_\pi(s)$
provides nice fits of the pion form factor data from $s=-0.25$ to $s=1$
GeV$^2$. It is shown that the coupling to $K \bar{K}$ has little effects, while
$\omg \pi^0$ improves significantly the fit quality below the $\phi$ mass. All
parameters, except for the subtraction polynomial coefficients are fixed from
the rest of the HLS phenomenology. The fits show consistency with the expected
behaviour of $F_\pi(s)$ at $s=0$ up to ${\cal O} (s^2)$ and with the phase
shift data on $\delta_1^1(s)$ from threshold to somewhat above the $\phi$ mass.
The $\omg$ sector is also examined in relation with recent data from CMD--2.
