A nonzero isotope effect for x=0.15, and an anomalous isotope effect, with the oxygen isotope-effect exponent O larger than the theoretical value of 0.5 for x=0.12, were reported in the past for the La2-xSrxCuO4 system. In view of the importance of understanding the mechanisms of high-temperature superconductivity, a reinvestigation of the isotope effect with more precise materials synthesis and isotope characterization is called for. We synthesized in flowing O218, or in flowing O216, copper-rich and stoichiometric versions of the La2-xSrxCuO4 materials at x=0.125 and x=0.15. We characterized the materials with x-ray diffraction, high-sensitivity, high-temperature mass spectrometry, and magnetic measurements. We found that in the stoichiometric materials, both at x=0.125 and x=0.15, the oxygen isotope-effect exponent, O 0.4. The copper-rich samples at x=0.125 have a larger isotope shift than the stoichiometric ones, due to a larger amount of the La1.67Sr0.33Cu2O5 nonsuperconducting second phase in the containing18 material, than in the containing16 material, which leaves the superconducting phase with a lower strontium concentration, which further lowers Tc. For the copper-rich x=0.15 material we found an oxygen isotope-effect exponent O=0.08. © 1992 The American Physical Society.