Germanium-tin-on-insulator (GSOI) has emerged as a new platform for three-dimensional (3D) photonic-integrated circuits (PICs). We report, to our knowledge, the first demonstration of GeSn dual-waveband resonant-cavity-enhanced photodetectors (RCE PDs) on GSOI platforms with resonance-enhanced responsivity at both 2 µm and 1.55 µm bands. 10% Sn is introduced to the GeSn absorbing layer to extend the detection wavelength to the 2 µm band. A vertical Fabry-Perot cavity is designed to enhance the responsivity. The measured responsivity spectra show resonance peaks that cover a wide wavelength range near both the 2 µm and conventional telecommunication bands. This work demonstrates that GeSn dual-waveband RCE PDs on a GSOI platform are promising for CMOS-compatible 3D PICs for optoelectronic applications in 2 µm and telecommunication bands.