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HgTe‐ZnTe strained type III superlattices have been grown for the first time using the molecular beam epitaxy technique. Three superlattices grown at 185 °C have been characterized by electron and x‐ray diffraction, infrared absorption, and Hall measurements. The presence of satellite peaks in the x‐ray spectra shows that the superlattices are of good quality despite the large lattice mismatch between HgTe and ZnTe (Δa/a=6.5%). These superlattices are p type and the hole mobilities are very high compared to those of the corresponding alloy. Such a phenomenon has already been reported for HgTe‐CdTe superlattices. Infrared transmission spectra show that HgTe‐ZnTe superlattices have narrower band gaps than equivalent HgZnTe alloys.