  We study rigidly rotating and pulsating $(m,n)$ strings in $AdS_3 \times S^3$
with mixed three form flux. The $AdS_3 \times S^3$ background with mixed three
form flux is obtained in the near horizon limit of $SL(2,Z)$-transformed
solution, corresponding to the bound state of NS5-branes and fundamental
strings. We study the probe $(m,n)-$string in this background by solving the
manifest $SL(2,Z)-$covariant form of the action. We find out the dyonic giant
magnon and single spike solutions corresponding to the equations of motion of a
probe string in this background and find out various relationships among the
conserved charges. We further study a class of pulsating $(m,n)$ string in
$AdS_3$ with mixed three form flux.
