  By measuring AC susceptibility using a very low amplitude of the AC field (<1
mG) it is shown that underdoped samples of La_(2-x)Sr_xCuO_4 (LASCO), are
diamagnetic in a temperature region above T_c up to a temperature T^*. This
behavior is only observed with AC fields along the c-axis whereas for fields in
the ab-plane no diamagnetism above Tc was detected. The diamagnetism is almost
frequency independent in the frequency range 0.1-10 kHz. At T* a broad step
anomaly in the specific heat is inferred through measurements of the elastic
constant c33. We suggest that the observed diamagnetism and the anomaly in the
elastic constant are associated with the existence of phase incoherent Cooper
pairs between Tc and T*.
