The transmission spectrum of fiber Bragg gratings with gratings planes tilted at a small angle (2°-10°) relative to the fiber axis shows a large number of narrowband cladding mode resonances within a 100 nm wide spectrum. When a gold coating with a thickness between 10 and 30 nm is deposited on the fiber, the transmission spectrum shows anomalous features for values of the outside medium refractive index between 1.4211 and 1.4499. These features are shown to correspond to the excitation of surface plasmon resonances at the external surface of the gold film.