The crystal and magnetic structures of RbMnF4 and KMnF 4 have been determined by neutron powder diffraction. The crystal symmetry of both compounds belongs to the layered perovskite structure and exhibits a pseudo-tetragonal unit cell, space group P21/a. The (MnF2F42/)- octahedra show a distortion induced by both steric and Jahn-Teller effects. They are also tilted by an angle which depends on the size of the alkali ion. KMnF4 orders as a noncollinear antiferromagnet below 5.2 +or- 0.1 K exhibiting four magnetic sublattices with an angle between the two spin directions of 17 degrees . RbMnF4 is a collinear antiferromagnet below 3.7 +or- 0.1 K. Interestingly enough and contrary to what is found for the K compound, there are two active irredu...