  Among promising sources of gravitational waves are long-lived nearly periodic
signals produced by rotating, asymmetric neutron stars. Depending on the
astrophysical scenario, the sources of asymmetry may have thermal, viscous,
elastic and/or magnetic origin. In this work we introduce a follow-up procedure
for an all-sky search for gravitational wave signals from rotating neutron
stars. The procedure denoted as Followup implements matched-filtering
$\mathcal{F}$-statistic method. We describe data analysis methods and
algorithms used in the procedure. We present tests of the Followup for
artificial signals added to white, Gaussian noise. The tests show a good
agreement with the theoretical predictions. The Followup will become part of
the Time-Domain $\mathcal{F}$-statistic pipeline that is routinely used for
all-sky searches of LIGO and Virgo detector data.
