  We study the transverse instability and dynamics of bright soliton stripes in
two-dimensional nonlocal nonlinear media. Using a multiscale perturbation
method, we derive analytically the first-order correction to the soliton shape,
which features an exponential growth in time -- a signature of the transverse
instability. The soliton's characteristic timescale associated with its
exponential growth,is found to depend on the square root of the nonlocality
parameter. This, in turn, highlights the nonlocality-induced suppression of the
transverse instability. Our analytical predictions are corroborated by direct
numerical simulations, with the analytical results being in good agreement with
the numerical ones.
