Data are presented for the first time on exclusive Pomeron-Pomeron interactions which produce a neutral strange and neutral antistrange particle pair in a central system X. In this paper, the system, X, is identified as one of the following neutral combinations; K[subscript]sps0K[subscript]sps0, K[subscript]sps0K[superscript]±[pi][superscript][minus or plus], [lambda][superscript]0[macron][lambda][superscript]0, [lambda][superscript]0[macron][lambda][superscript]0*. These data were obtained in proton-proton collisions at √s = 62 GeV at the CERN ISR. The triggering systems used to obtain these data are described, followed by a description of the data. The central system mass distributions are presented along with differential mass cross section estimates. A broad enhancement is seen in the K[subscript]sps0K[subscript]sps0 system at a mass of 1.2 GeV, and is likely to have the quantum numbers J[superscript]PC = 0[superscript]++. Total cross section estimates of 1.3 ±.64 [mu] b in the K[subscript]sps0K[subscript]sps0 system,.44 ±.14 [mu] b in the K[subscript]sps0K[superscript]±[pi][superscript][minus or plus] system,.20 ±.14 [mu] b in the [lambda][superscript]0[macron][lambda][superscript]0 system, and.13 ±.06 [mu] b in the [lambda][superscript]0[macron][lambda][superscript]0* system are obtained.