Anomalous low friction of hydrogen-free tetrahedral hybridized carbon (ta-C) coated surfaces lubricated by pure glycerol was observed at 80°C. In the presence of glycerol, the friction coefficient is below 0.01 at steady state, corresponding to so-called superlubricity regime. This new mechanism of superlow friction is attributed to easy glide on tribo-formed OH-terminated surfaces. In addition to the formation of OH-terminated surfaces but at a lower temperature, we show here some evidence that superlow friction of polyhydric alcohols could also be associated with tribo-induced degradation of glycerol, producing a nanometer-thick film containing organic acids and water. Second, we show novel outstanding superlubricity of steel surfaces directly lubricated by a solution of myo-inositol in glycerol at ambient temperature (25°C). For the first time, under boundary lubrication at high contact pressure, friction of steel is below 0.01 in the absence of any long chain polar molecules. Mechanism is still unknown but could be associated with friction-induced dissociation of glycerol and interaction with steel surface.