  Presented are the first measurements of the transverse single-spin
asymmetries ($A_N$) for neutral pions and eta mesons in $p$+Au and $p$+Al
collisions at $\sqrt{s_{_{NN}}}=200$ GeV in the pseudorapidity range
$|\eta|<$0.35 with the PHENIX detector at the Relativistic Heavy Ion Collider.
The asymmetries are consistent with zero, similar to those for midrapidity
neutral pions and eta mesons produced in $p$+$p$ collisions. These measurements
show no evidence of additional effects that could potentially arise from the
more complex partonic environment present in proton-nucleus collisions.
