  In the present work, we have done a systematic shell model study of $N=82$
and $N=126$ isotones. For the $N=82$ isotones, we have performed calculations
using SN100PN interaction, while for $N=126$ isotones, we have used KHPE
interaction. Similarities between these two isotonic chains have been reported,
using the strong resemblance between the high-$j$ orbitals. Apart from the
nuclear spectroscopic properties, we have also explained different isomeric
states in these two regions. In the $N$ =82 region, we have mainly discussed
the properties of the $6^+$ and $17/2^+$ isomers, while in the $N=126$ region
for $8^+$, $11^-$, $21/2^-$ and $29/2^+$ isomers. We have reported $B(E2)$,
$B(E3)$, $g$-factor, and quadrupole moments of the isomeric states for
comparison in these two isotonic chains.
