The development of short-and long-range magnetic order induced in a frustrated zigzag ladder compound SrDy 2 O 4 by an applied field is studied using neutron-diffraction techniques. In zero field, SrDy 2 O 4 lacks long-range magnetic order down to temperatures as low as 60 mK, and the observed powder-neutron-diffraction (PND) patterns are dominated by very broad diffuse scattering peaks. Single-crystal neutron diffraction reveals that the zero-field magnetic structure consists of a collection of antiferromagnetic chains running along the c axis and that there is very little correlation between the chains in the ab plane. In an applied magnetic field, the broad diffuse scattering features in PND are gradually replaced by much sharper peaks, however, the pattern remains rather complex, reflecting the highly anisotropic nature of SrDy 2 O 4 . Single-crystal neutron diffraction shows that a moderate field applied along the b axis induces an up-up-down magnetic order associated with a 1 3 -magnetization plateau, in which magnetic correlation length in the ab plane is significantly increased, but it nevertheless remains finite. The resolution-limited k = 0 peaks associated with a ferromagnetic arrangement appear in powder and single-crystal neutron-diffraction patterns in fields of 2.5 T and above.