  The dispersion law for the linear waves in the quasi-one-dimensional array of
inductively coupled Josephson junctions (JJ) is derived. The array has a
multiladder structure that consists of the finite number of rows ($N\ge 2$) in
$Y$ direction and is infinite in $X$ direction. The spectrum of the linear
waves (Josephson plasmons) consists of $2N-1$ branches. Among these branches
there is a $N$-fold completely flat degenerate one that coincides with the
Josephson plasma frequency. The remaining $N-1$ branches have a standard
Josephson plasmon dispersion law typical for 1D JJ arrays. Application of the
uniform dc bias on the top of each vertical column of junctions lifts the
degeneracy and only one flat branch remains unchanged. The rest of the
previously flat branches become weakly dispersive. The parameter range where
the flatness of these branches is maximal has been discussed.
