Fiber laser sources in the spectral range near 1.7–1.8 μm are in highly demand for a lot of applications. We propose and theoretically investigate a dual-wavelength switchable Raman tungsten-tellurite fiber laser in the 1.7–1.8 µm range which can produce two stable modes at frequencies separated by ~7 THz with a pump at 1.55 µm. The Raman waves shifted by 19.8 THz (mode 1) and 27.5 THz (mode 2) from the pump frequency can be generated near two different maxima of the Raman gain spectrum (gain is higher at 19.8 THz and twice lower at 27.5 THz). We numerically simulate two-mode Raman lasing with allowance for energy transfer from the pump wave to modes 1 and 2, and from mode 1 to mode 2 due to inelastic Raman scattering. Diagrams of generation regimes depending on system parameters are constructed. We demonstrate controlled switching between two modes by changing the pump power. For the same intracavity losses for both Raman modes at relatively low pump powers, only mode 1 is generated. At medium pump power, generation occurs simultaneously in both modes. At relatively high pump power, only mode 2 is generated near the weaker maximum. This effect seems surprising, but a rigorous explanation with allowance for the nonlinear interaction between mode 1 and mode 2 is found. When losses for one of the modes change, switching of the generated regimes is also predicted.