Taking subadditivity as a main axiom Artzner et.al.(1997, 1999) introduced the so-called coherent risk measures. Song and Yan (2006) introduced risk measures which are comonotonically subadditive or convex. In this talk I will present a recent work with Yongsheng Song, in which we proposed some new risk measures, which are not only comonotonically subadditive or convex, but also respect the (first) stochastic dominance or stop-loss order..