We investigate how perturbations propagate up and down a food chain with and without self-interaction and omnivory. A source of perturbation is a shift in death rate of a trophic level, and the measure of perturbation is the difference between the perturbed and unperturbed steady-state populations. For Lotka–Volterra food chains with linear functional response, we show analytically that both intraspecific competition and intraguild predation can either dampen or enhance the propagation of perturbations, thus stabilizing or destabilizing the food web. The direction of the effect depends on the position of the source of perturbation, as well as on the position of the additional competitive and predatory links . These conclusions are confirmed numerically for a food chain with more realistic type II functional response. Our results extend and confirm previous numerical results for short food chains and support positions on both sides in the long-standing debate on the effect of intraspecific competition and omnivory on the stability of trophic systems.