In this work, we report the experimental observation of supercontinua generation in two kinds of suspended-core microstructured soft-glass optical fibers. Low loss, highly nonlinear, tellurite and As2S3 chalcogenide fibers have been fabricated and pumped close to their zero-dispersion wavelength in the femtosecond regime by means of an optical parametric oscillator pumped by a Ti:Sapphire laser. When coupled into the fibers, the femtosecond pulses result in 2000-nm bandwidth supercontinua reaching the Mid-Infrared region and extending from 750 nm to 2.8 µm in tellurite fibers and 1 µm to 3.2 µm in chalcogenide fibers, respectively.