It has been shown recently by B. D. Jones et al 1) that most (~ 80%) of the hyperfragments produced in the interactions of 800 MeV/c K" mesons with emulsion nuclei are of short range (< 5 p.m) and possess mass numbers between A = 60 and A = 90. According to the model proposed in •'^), a A° hyperon created in the cascade process initiated by a K" meson may sometimes become trapped in the heavy highly excited residual nucleus. The A° hyperon may then be emitted either free or bound to a nuclear fragment during the evaporation stage. Sometimes, however, it will remain trapped until its decay in the heavy spallation product of the re action, forming a heavy hyperfragment. This let ter gives the results of a similar study using K" mesons of 1.3 and 1.5 GeV/c. Three stacks of ILford K5 emulsion were exposed to the separated K" meson beams of momentum 1.3 GeV/c (two stacks) and 1.5 GeV/c (one stack) which were available at CER N early in 1962. The plates were area scanned for nuclear interactions produced by beam particles; 17871 stars were found at 1.3 GeV/c and 13001 at 1.5 GeV/c Each star was examined under high magnification to de tect the possible présence of two centers. AU prongs from each star were foUowed in the emul sion sheet containing the event and any secondary interaction was noted. Of the double stars found in this search, 746 at 1.3 GeV/c and 532 at 1.5 GeV/c were classified as due to the production * Chercheur agréé â l'Institut Interuniversitaire des S ciences Nucléaires Belgique. ** Now at the Enrico Fermi Institute for Nuclear S tudies University of Chicago.