  We propose a new collider probe for axion-like particles (ALPs), and more
generally for pseudo-Goldstone bosons: non-resonant searches which take
advantage of the derivative nature of their interactions with Standard Model
particles. ALPs can participate as off-shell mediators in the $s$-channel of $2
\to 2$ scattering processes at colliders like the LHC. We exemplify the power
of this novel type of search by deriving new limits on ALP couplings to gauge
bosons via the processes $p p \to Z Z$, $p p \to \gamma \gamma$ and $p p \to j
j$ using Run 2 CMS public data, probing previously unexplored areas of the ALP
parameter space. In addition, we propose future non-resonant searches involving
the ALP coupling to other electroweak bosons and/or the Higgs particle.
