We study the orbits in the MOND theory within a dwarf galaxy of mass M _ { d } \sim 10 ^ { 8 } M _ { \odot } at a distance of \sim 100 kpc from a neighboring galaxy of mass M _ { g } = 5 \times 10 ^ { 11 } M _ { \odot } , such as ours .
It is assumed that a second mass m < < M _ { d } is gravitationally bound to M _ { d } by a previously calculated potential for the MOND theory .
This potential is obtained for a free falling mass M _ { d } in a constant external gravitational acceleration field \nabla \phi _ { g } .
The numerical technique of surfaces of section is used to study the stability of the phase-space orbits in the dwarf galaxy .
Equatorial orbits with sufficiently small eccentricities e < 0.65 are found to be stable with respect to small changes in the initial conditions .
( The equatorial plane is perpendicular to the direction of \nabla \phi _ { g } , which is along the line joining M _ { d } and M _ { g } . )
For decreasing values of the conserved component of the angular momentum , in the direction of \nabla \phi _ { g } , equatorial stability is lost .