Using the first-order normalized equations describing the heliocentric cometary motion perturbed by the Galactic tides, we identify `stationary solutions' with constant values of the eccentricity, inclination, argument of perihelion and longitude of the ascending node in the reference frame rotating with the Galaxy. The families found involve circular orbits, orbits in the Galactic equatorial plane, rectilinear orbits normal to the equatorial plane, elliptic orbits symmetric with respect to the direction to the Galactic Centre or to its perpendicular, and asymmetrically oriented elliptic orbits. Linear stability of the stationary solution is studied analytically and confirmed by numerical experiments. Most, but not all, of the unstable solutions prove chaotic with the Lyapunov times at least 100Myr.