  Targeted searches of continuous waves from spinning neutron stars normally
assume that the frequency of the gravitational wave signal is at a given known
ratio with respect to the rotational frequency of the source, e.g. twice for an
asymmetric neutron star rotating around a principal axis of inertia. In fact
this assumption may well be invalid if, for instance, the gravitational wave
signal is due to a solid core rotating at a slightly different rate with
respect to the star crust. In this paper we present a method for {\it
narrow-band} searches of continuous gravitational wave signals from known
pulsars in the data of interferometric detectors. This method assumes source
position is known to high accuracy, while a small frequency and spin-down range
around the electromagnetic-inferred values is explored. Barycentric and
spin-down corrections are done with an efficient time-domain procedure.
Sensitivity and computational efficiency estimates are given and results of
tests done using simulated data are also discussed.
