We study numerically and experimentally multiple-wavelength operation of an erbium-doped figure-eight fiber laser including a multiple-bandpass optical filter formed by two concatenated fiber tapers. Both continuous-wave and pulsed operations are considered. In the continuous-wave regime, stable long-term operation at multiple closely spaced wavelengths is only obtained if fine adjustments of the cavity losses are performed. Under these conditions, simultaneous lasing at up to four wavelengths separated by 1.5 nm was observed experimentally. Tunable singlewavelength operation over more than 20 nm is also observed in the continuous-wave regime. In the passive mode locking regime, numerical simulations indicate that mechanisms involving the filter losses and the nonlinear transmission characteristic of the NOLM contribute in principle to stabilize dual-wavelength operation, allowing less demanding cavity loss adjustments. In this regime, the problem of synchronization between the pulse trains generated at each wavelength adds an additional dimension to the problem. In presence of cavity dispersion, the pulses at each wavelength tend to be asynchronous if the wavelength separation is large, however they can be synchronous in the case of closely spaced wavelengths, if cross-phase modulation is able to compensate for the dispersion-induced walkoff. Experimentally, fundamental and 2nd-order harmonic mode locking was observed, characterized by the generation of noise-like pulses. Finally, a regime of multi-wavelength passive Q-switching was also observed. We believe that this work will be helpful to guide the design of multiple-wavelength fiber laser sources, which are attractive for a wide range of applications including Wavelength Division Multiplexing transmissions, signal processing and sensing. Keywords: Nonlinear Optical Loop Mirror, Wavelength filtering devices, Mode-locked fiber lasers, Erbium fiber lasers