We report on pseudomorphic MBE growth of CdTe/Zn(Mg)(Se)Te quantum dot (QD) structures on InAs (100) substrates and studies of their structural and optical properties. The QDs were fabricated by using a thermal activation technique comprising deposition of a strained CdTe 2D layer, covering it with amorphous Te, followed by fast thermal desorption of the Te layer, which results in a 2D-3D RHEED pattern transition. The QDs exhibit the surface density as low as similar to 10(10) cm(-2). The influence of MBE growth parameters and the structure design on photoluminescence properties of the QDs are discussed. Single QD photoluminescence was observed at T=8 K from the 200-nm-wide mesa-structures made of the CdTe QD structures, and the antibunching effect with g((2))(0)= 0.16 +/- 0.04 was demonstrated. The peculiarities of MBE growth of ZnTe/MgTe/MgSe short-period superlattices nearly lattice-matched to InAs, which could serve as wide gap barriers for efficient electron and hole confinement in the CdTe/Zn(Mg)(Se) Te QDs, are also described. (C) 2016 Elsevier B.V. All rights reserved.