  We show that, under rather general assumptions, the phase diagram of a
quasi-one-dimensional repulsive Fermi system consists of two ordered phases:
the density wave, spin or charge, and the superconductivity. It is demonstrated
that the symmetry of the superconducting order parameter is a non-universal
property sensitive to microscopic details of the model. Three potentially
stable superconducting states are identified: they are triplet $f$-wave,
singlet $d_{x^2-y^2}$-wave, and $d_{xy}$-wave. Presence of multiple competing
superconducting states implies that for a real material this symmetry is
difficult to predict theoretically and hard to probe experimentally, since
artifacts of theoretical approximations or variations in experimental
conditions could tip the balance between the superconducting phases.
