  The Kovacs protocol, based on the temperature shift experiment originally
conceived by A.J. Kovacs for glassy polymers, is implemented in an exactly
solvable dynamical model. This model is characterized by interacting fast and
slow modes represented respectively by spherical spins and harmonic oscillator
variables. Due to this fundamental property, the model reproduces the
characteristic non-monotonic evolution known as the ``Kovacs effect'', observed
in polymers, in granular materials and models of molecular liquids, when
similar experimental protocols are implemented.
