  Reduced dielectric screening in two-dimensional materials enables bound
excitons, which modifies their optical absorption and optoelectronic response
even at room temperature. Here, we demonstrate the existence of excitons in the
bandgap of the monolayer family of the newly discovered synthetic MoSi$_2$Z$_4$
(Z = N, P, and As) series of materials. All three monolayers support several
bright and strongly bound excitons with binding energies varying from 1 eV to
1.35 eV for the lowest energy exciton resonances. On increasing the pump
fluence, the exciton binding energies get renormalized, leading to a
redshift-blueshift crossover. Our study shows that the MoSi$_2$Z$_4$ series of
monolayers offer an exciting test-bed for exploring the physics of strongly
bound excitons and their non-equilibrium dynamics.
