  Magnetic dc susceptibility ($\chi$) and electron spin resonance (ESR)
measurements in the paramagnetic regime, are presented. We found a Curie-Weiss
(CW) behavior for $\chi$(T) with a ferromagnetic $\Theta = 446(5)$ K and
$\mu_{eff} = 4.72(9) \mu_{B}/f.u.$, this being lower than that expected for
either $Fe^{3+}(5.9\mu_{B})$ or $Fe^{2+}(4.9\mu_{B})$ ions. The ESR g-factor $g
= 2.01(2)$, is associated with $Fe^{3+}$. We obtained an excellent description
of the experiments in terms of two interacting sublattices: the localized
$Fe^{3+}$ ($3d^{5}$) cores and the delocalized electrons. The coupled equations
were solved in a mean-field approximation, assuming for the itinerant electrons
a bare susceptibility independent on $T$. We obtained $\chi_{e}^{0} = 3.7$
$10^{-4}$ emu/mol. We show that the reduction of $\mu_{eff}$ for $Fe^{3+}$
arises from the strong antiferromagnetic (AFM) interaction between the two
sublattices. At variance with classical ferrimagnets, we found that $\Theta$ is
ferromagnetic. Within the same model, we show that the ESR spectrum can be
described by Bloch-Hasegawa type equations. Bottleneck is evidenced by the
absence of a $g$-shift. Surprisingly, as observed in CMR manganites, no
narrowing effects of the ESR linewidth is detected in spite of the presence of
the strong magnetic coupling. These results provide evidence that the magnetic
order in $Sr_{2}FeMoO_{6}$ does not originates in superexchange interactions,
but from a novel mechanism recently proposed for double perovskites.
