Abstract: The new families of superconducting compounds ''1201'' (Hg0.4Pr0.6Sr2CuO4+delta), ''1212'' (Hg0.4Pr0.6Sr2(Ca1-x-ySrxPry) Cu2O6+delta), and ''1222'' (Hg0.4Pr0.6Sr2(Pr1.7Sr0.3)(2)Cu2O8+delta) all show ordering between praseodymium and mercury in the (Hg,Pr)O-delta plane, reducing the symmetry from tetragonal to orthorhombic or even to monoclinic. In the 1201 compound the ordered superstructure can be described as O-I (a(I) approximate to 2a(p), b(I), approximate to a(p), c(I) approximate to c(1201)). In the 1212 compound two distinct superstructures are identified, O-I (a(I) approximate to 2a(p), b(II) approximate to a(p), c(I) approximate to c(1212)) and O-II (a(II) approximate to 2a(p), b(II) approximate to a(p), c(II) approximate to 2c(1212)). In some compounds, such as Hg0.4Pr0.6Sr2(Ca0.4Sr0.4Pr0.2) Cu2O6+delta, the Hg-Pr ordering is only present in microdomains, but due to an ordering between Sr layers and Ca layers, the c-axis doubles and one obtains a tetragonal superstructure T-III (a(III) approximate to a(p), c(III) approximate to 2c(1212)). In the 1222 compound, ordering in the (Pr,Hg)O-delta plane is very defective; a large number of translation defects actually reduce the symmetry to triclinic. (C) 1995 Academic Press, Inc.