  We study the existence of steady solutions of ideal magnetofluid systems
(ideal MHD and ideal Euler equations) without continuous Euclidean symmetries.
It is shown that all nontrivial magnetofluidostatic solutions are locally
symmetric, although the symmetry is not necessarily an Euclidean isometry.
Furthermore, magnetofluidostatic equations admit both force-free (Beltrami
type) and non-force-free (with finite pressure gradients) solutions that do not
exhibit invariance under translations, rotations, or their combination.
Examples of smooth solutions without continuous Euclidean symmetries in bounded
domains are given. Finally, the existence of square integrable solutions of the
tangential boundary value problem without continuous Euclidean symmetries is
proved.
