Two series of Mn-substituted rare-earth zinc arsenides RE1-yMnxZn2-xAs2 (RE = Eu-Lu) and RE2-yMnxZn4-xAs4 (RE = La-Nd, Sm, Gd) were prepared by reaction of the elements at 750 degrees C. Both series are derived from ideal empirical formula REM2As2 (M = Mn, Zn) and adopt crystal structures related to the trigonal CaAl2Si2-type (space group P (3) over bar m1) in which hexagonal nets of RE atoms and (M2As2] slabs built up of edge-sharing M-centered tetrahedra are alternately stacked along the c-direction. For compounds with divalent RE components (Eu, Yb), the fully stoichiometric and charge-balanced formula REM2As2 is obtained, with Mn and Zn atoms statistically disordered within the same tetrahedral site. For compounds with trivalent RE components, the RE sites become deficient, and the Mn atoms are segregated from the Zn atoms in separate tetrahedral sites. Within the series RE1-yMnxZn2-xAs2 (Gd-Tm, Lu), the parent CaAl2Si2-type structure is retained, and the Mn atoms are disordered within partially occupied interstitial sites above and below [Zn2-xAs2] slabs. Within the series RE2-yMnxZn4-xAs4 (RE = La-Nd, Sm, Gd), the c-axis becomes doubled as a result of partial ordering of Mn atoms between every other pair of [Zn2-xAs2] slabs. Attempts to synthesize Gd-containing solid solutions with the charge-balanced formula Gd0.67MnxZn2-xAs2 suggested that these phases could be formed with up to 50% Mn substitution. Band structure calculations reveal that a hypothetical superstructure model with the formula La1.33MnZn3As4 would have no gap at the Fermi level and that slightly lowering the electron count alleviates antibonding Mn-As interactions; a spin-polarized calculation predicts nearly ferromagnetic half-metallic behavior. X-ray photoelectron spectroscopy confirms the presence of divalent Mn in these compounds.