We have synthesized new Ba-free Hg-based superconductors (Hg(1-x)M(x))Sr-2(Ca1-yYy)(n-1)CunOz (n=1,2). These compounds are chemically and structurally stabilized by partial substitution of the elements M=Cr, Mo and Re. While M-free compounds were multi-phased and superconducting volume fractions were less than 1%, M-doped Hg 1201-type compounds, (Hg(1-x)M(x))Sr2CuOz, were nearly single phased and found to be superconductors with Tc's of 50 similar to 70K. Furthermore, by partially substituting Y for Ca, we have synthesized 1212-type compounds (Hg(1-x)M(x))Sr-2(Ca1-yYy)Cu2Oz with Tc's similar to 100K. In contrast to the Ba-containing compounds, the present materials are insensitive to open air during the synthesis and also quite stable after the preparation.