  We study numerically the nonlinear stability of {\it excited} fermion-boson
stars in spherical symmetry. Such compound hypothetical stars, composed by
fermions and bosons, are gravitationally bound, regular, and static
configurations described within the coupled Einstein-Klein-Gordon-Euler
theoretical framework. The excited configurations are characterized by the
presence in the radial profile of the (complex, massive) scalar field -- the
bosonic piece -- of at least one node across the star. The dynamical emergence
of one such configuration from the accretion of a cloud of scalar field onto an
already-formed neutron star, was numerically revealed in our previous
investigation. Prompted by that finding we construct here equilibrium
configurations of excited fermion-boson stars and study their stability
properties using numerical-relativity simulations. In addition, we also analyze
their dynamical formation from generic, constraint-satisfying initial data.
Contrary to purely boson stars in the excited state, which are known to be
generically unstable, our study reveals the appearance of a cooperative
stabilization mechanism between the fermionic and bosonic constituents of those
excited-state mixed stars. While similar examples of stabilization mechanisms
have been recently discussed in the context of $\ell-$boson stars and
multi-field, multi-frequency boson stars, our results seem to indicate that the
stabilization mechanism is a purely gravitational effect and does not depend on
the type of matter of the companion star.
