  In U(1) extensions of the Minimal Supersymmetric extension of the Standard
Model there is a simple mechanism that leads to a heavy Z' boson with a mass
which is substantially larger than the supersymmetry breaking scale. This
mechanism may also result in a pseudoscalar state that is light enough for
decays of the 125 GeV Standard Model-like Higgs boson into a pair of such
pseudoscalars to be kinematically allowed. We study these decays within E6
inspired supersymmetric models with an exact custodial symmetry that forbids
tree-level flavor-changing transitions and the most dangerous baryon and lepton
number violating operators. We argue that the branching ratio of the lightest
Higgs boson decays into a pair of the light pseudoscalar states may not be
negligibly small.
