The space motions of Mira variables are derived from radial velocities, Hipparcos proper motions and a period–luminosity relation. The previously known dependence of Mira kinematics on the period of pulsation is confirmed and refined. In addition, it is found that Miras with periods in the range 145–200 d in the general Solar neighbourhood have a net radial outward motion from the Galactic Centre of 75±18 km s−1. This, together with a lag behind the circular velocity of Galactic rotation of 98±19 km s−1, is interpreted as evidence for an elongation of their orbits, with their major axes aligned at an angle of ∼17° with the Sun–Galactic Centre line, towards positive Galactic longitudes. This concentration seems to be a continuation to the Solar circle and beyond of the bar-like structure of the Galactic bulge, with the orbits of some local Miras probably penetrating into the bulge. These conclusions are not sensitive to the distance scale adopted. A further analysis is given of the short-period (SP) red group of Miras discussed in companion papers in this series. In Appendix A the mean radial velocities and other data for 842 oxygen-rich Mira-like variables are tabulated. These velocities were derived from published optical and radio observations.