Liquid phase epitaxial (LPE) growth from Hg-rich solution is investigated in the case of HgTe-based quaternary semiconductors Hg1-x-yCdxZnyTe and Hg1-x-yCdxMnyTe and the ternary Hg1-xCdxTe. In contrast to the results for Hg1-xCdxTe, the LPE growth can give crystals of quaternary alloys with excellent compositional uniformity. The uniform compositional profiles of the epilayers are revealed by electron probe microanalysis, both in the plane and along the growth direction. The growth of Hg1-xCdxTe by the same LPE method yields a large compositional gradient along the growth direction. Thus we have clearly demonstrated that homogeneity of epilayers are improved by incorporation of Zn or Mn during the crystal growth. A typical sample of as-grown Hg1-x-yCdxZnyTe, with x=0.17 and y=0.10 (E(g) approximate to 320 meV at 77 K), showed n-type conduction with a carrier concentration of 1x10(16) cm(-3) and a mobility of 9x10(2) cm(2)/V s at 77 K. As-grown Hg1-x-yCdxMnyTe showed n-type conduction with a carrier concentration of 3x10(14) cm(-3) and a mobility of 8x10(4) cm(2)/V s at 77 K for a typical sample with x=0.16 and y=0.009 (E(g) approximate to 150 meV at 77 K).