A charged particle exposed to an oscillating electric field experiences a force proportional to the cycle-averaged intensity gradient. This so-called ponderomotive force1 plays a major part in a variety of physical situations such as Paul traps2, 3 for charged particles, electron diffraction in strong (standing) laser fields4, 5, 6 (the Kapitza–Dirac effect) and laser-based particle acceleration7, 8, 9. Comparably weak forces on neutral atoms in inhomogeneous light fields may arise from the dynamical polarization of an atom10, 11, 12; these are physically similar to the cycle-averaged forces. Here we observe previously unconsidered extremely strong kinematic forces on neutral atoms in short-pulse laser fields. We identify the ponderomotive force on electrons as the driving mechanism, leading to ultrastrong acceleration of neutral atoms with a magnitude as high as 1014 times the Earth's gravitational acceleration, g. To our knowledge, this is by far the highest observed acceleration on neutral atoms in external fields and may lead to new applications in both fundamental and applied physics.