  This paper is devoted to the analysis of (m,n)-string in stringy
Newton-Cartan background. We start with the Hamiltonian constraint for
(m,n)-string in general background and perform limiting procedure on metric and
NSNS and Ramond-Ramond two form background that leads to stringy Newton-Cartan
gravity. We also analyze conditions that these background fields have to obey
in order to define consistent world-sheet (m,n)-theory. We also discuss
D1-brane with dynamical electric field in stringy Newton-Cartan gravity.
