Average stellar orbits of the Galactic disk may have some small intrinsic ellipticity which breaks the exact axisymmetry and there may also be some migration of stars inwards or outwards. Both phenomena can be detected through kinematic analyses. We use the red clump stars selected spectroscopically from the APO Galactic Evolution Experiment, with known distances and radial velocities, to measure the radial component of the Galactocentric velocities within 5 kpc < R < 16 kpc, | b| \lt 5^\circ , and within 20° from the Sun–Galactic center line. The average Galactocentric radial velocity is VR = (1.48 ± 0.35)[R(kpc) ‑ (8.8 ± 2.7)] km s‑1 outwards in the explored range, with a higher contribution from stars below the Galactic plane. Two possible explanations can be given for this result: (i) the mean orbit of the disk stars is intrinsically elliptical with a Galactocentric radial gradient of eccentricity around 0.01 kpc‑1 or (ii) there is a net secular expansion of the disk, in which stars within R ≈ 9–11 kpc are migrating to the region R ≳ 11 kpc at the rate of ∼2 M⊙ yr‑1, and stars with R ≲ 9 kpc are falling toward the center of the Galaxy. This migration ratio would be unattainable for a long time and should decelerate, otherwise the Galaxy would fade away in around 1 Gyr. At present, both hypotheses are speculative and one would need data on the Galactocentric radial velocities for other azimuths different to the center or anticenter in order to confirm one of the scenarios.