Development of coherent sources, wideband thulium-doped fiber amplifiers, and fiber components has opened up the wavelength region around 2000 nm for optical communications, sensing, and medical surgery. However, several key functionalities that are critical to enable these applications are not yet well developed and, therefore, need attention. Here, we present demonstration of two critical signal processing tasks viz: (1) tunable delay and (2) tunable narrowband filter, which are important for enabling optical communications using wavelengths around 2000 nm. We exploit stimulated Brillouin scattering (SBS) in a 100 m long SM1950 fiber to report the first demonstration of slow-light based tunable delay around 2000 nm. For a 35 ns input pulse, we tune the delay up to a maximum of 18.8 ns, which corresponds to a relative delay of ∼0.5, by varying the pump power to achieve a maximum gain of 12.6 dB. For the 1550 nm wavelength regime, it has been shown that the Brillouin slow-light typically results in a delay of 1 ns/dB, which is less than the 1.67 ns/dB obtained at 2000 nm. For the same gain, the large delay at 2 μm compared to 1.55 μm results from the narrow gain bandwidth (∼22 MHz) of the SBS process in this wavelength regime. Using the narrow gain bandwidth of SBS, we present a proof-of-concept experiment to demonstrate filtering of individual comb lines in a comb with frequency spacing <50 MHz. Demonstration of tunable narrowband filter and delay enables optical signal processing and line-by-line control of comb lines at 2 μm.