A variety of instrumental effects can corrupt the observable quantities in optical or nulling stellar interferometry.
One such effect is parasitic interference, which can occur inside an interferometric instrument. Because of
diffraction effects related to beam propagation along finite size optics, or parasitic reflections inside transmitting
optics, a coherent crosstalk may occur between the beams and create a parasitic interference pattern superimposed
on the genuine one. We developed an analytical approach to describe the impact of this effect on the observables
of classical and nulling stellar interferometers. Considering classical interferometry, we show that differential
phase and closure phase are both corrupted, depending on the crosstalk level and the residual piston between
the beams. Considering typical specifications of piston correction of ground-based interferometers (≈ 100 nm),
the detection of hot Jupiter-like planets by differential phase implies a tolerance on the parasitic flux to about
5% of the incident intensity. Also, we show that the closure phase relation does not remove this parasitic
contribution. The corresponding corrupted closure phase is not zero for an unresolved source, and depends on
the residual piston. Considering nulling interferometry, we show that parasitic effects modify the transmission
map level, depending on the crosstalk level and the phase shift between primary and secondary beams. In the
extreme case of a pi-phase shift, the crosstalk effect implies a decrease of the final output signal-to-noise ratio.
Numerical simulations, adapted to handle consistently crosstalk, are then performed to estimate this degradation
and validate our theoretical study.