Abstract: In this paper, we suggest a new class of failure distributions, which is called HDMRL class. A distribution function F（x）belongs to HDMRL class, if \left\\frac1\mu \int_t^\infty \barF(x) d x\right\^1 / t is monotone non-increasing in t,μ being the finite expectation of F（x）. Similarly, the dual class HIMRL is also defined. The relationship between HDMRL class and others is given. The close property under the reliability operations and the preservation properties under some shock models are cosidered. The equivalent relationship between the distribution of HDMRL class and its Lapla1e-Stieltje transformation is also given.