The nonlinear refractive index for 10 types of recently developed new soft glasses was measured under the same conditions using a pulsed Nd:YAG laser operating at 1064 nm with a 35 ps pulse duration. The study included various types of oxide-based soft glasses commonly used for nonlinear fiber optics, such as lead silicate, borosilicate, phosphatate, tellurite and heavy metal oxide glasses. All studied glasses have good rheological properties, and are suitable for further multi-step thermal processing, including fabrication of nonlinear photonic crystal fibers. As reference samples, standard fused silica glass and commercially available lead silicate glasses were used. The standard Z-scan setup was employed, with both “open-” and “closed-aperture” types of measurement. We show that nonlinearities of some benchmarked thermally stable heavy metal oxide glasses are comparable to more expensive and very fragile chalcogenide glasses.