We have made Co-59 NMR measurements to microscopically study magnetic properties of the two-dimensional layered perovskite cobalt oxides, La2-xSrxCoO4 (0.5 less than or equal to x less than or equal to 1). The temperature dependence of the Co-59 Knight shift K-59 clearly shows that La2-xSrxCoO4 (0.5 less than or equal to s less than or equal to 1) are paramagnetic above 4.2 K. From the analysis of the K-59 versus magnetic susceptibility plots, the hyperfine coupling constant was found to change at x(c) similar to 0.75, indicating that the spin state changes at this critical concentration. (C) 1999 Elsevier Science B.V. All rights reserved.