SQUID measurements of the time decay of the thermoremanent magnetization (field-cooled in 1000 Oe) at long time scale, 102 < t < 105 s, are presented for MBE grown Cd 0.50 Mn 0.50 Τe. We found that for both thin (32 A) and thick (2500 A) layers the spin-glass dynamics is characterized by a similar value of k = -(1/Tf)(dTf/dlog t) > 0.05, indicating the absence of the phase transition at nonzero temperature under the experimental conditions.PACS numbers: 75.50.11r, 75.50.Lk Diluted magnetic semiconduction (DMS), such as Cd1-x Mn x Te, are disordered Heisenberg antiferromagnets in which both lattice favoured fustration and randomness may lead to a spin-glass-like state at low temperatures [1]. Recent progress in fabrication techniques, such as molecular beam epitaxy (MBE) [2], has made it possible to investigate properties of the spin-glass phase of DMS in the form of very thin layers [3], thus enabling us to address the problem of the lower critical dimensionality for this system [4]. To face this problem we investigated low temperature properties of Cd0.50Mn0.50Τe layers with varying thicknesses: 5, 10, 15, and 20 monolayers (MLs). In order to improve the signal-tonoise ratio, the samples were grown in the form of superlattices with about 200 periods, and with nonmagnetic CdTe spacers thick enough (16 ML 50 Å) to preclude the interlayer magnetic coupling. We found so far that the freezing temperature Tf does depend on the width of the magnetic layer w, namely it scales with Τ as Tf α 0 0 . 8 [4], i.e. in the way theoretically expected for thin layered spin glasses measured over a long yet limited time scale [5].Within the droplet-scaling theory the observation time t is directly related to a length scale, L(t), on which the dynamics is probed. Thus, as long as L(t) is smaller than w the spin-glass film displays 3D dynamic behaviour and crosses over