  We study the effect of a uniform pseudomagnetic field, induced by a strain in
a monolayer and double layer of gapped graphene, acting on excitons. For our
analysis it is crucial that the pseudomagnetic field acts on the charges of the
constituent particles of the excitons, i.e., the electrons and holes, the same
way in contrast to a magnetic field. Moreover, using a circularly polarized
laser field, the electrons and the holes can be excited only in one valley of
the honeycomb lattice of gapped graphene. This breaks the time-reversal
symmetry and provides the possibility to observe the various Quantum Hall
phenomena in this pseudomagnetoexciton system. Our study poses a fundamental
problem of the quantum Hall effect for composite particles and paves the way
for quantum Hall physics of pseudomagnetoexcitons.
