We have observed the remnant of supernova SN 1987A ( SNR 1987A ) , located in the Large Magellanic Cloud ( LMC ) , to search for periodic and/or transient radio emission with the Parkes 64 m-diameter radio telescope . We found no evidence of a radio pulsar in our periodicity search and derived 8 \sigma upper bounds on the flux density of any such source of 31 \mu Jy at 1.4 GHz and 21 \mu Jy at 3 GHz . Four candidate transient events were detected with greater than 7 \sigma significance , with dispersion measures ( DMs ) in the range 150 to 840 cm ^ { -3 } pc . For two of them , we found a second pulse at slightly lower significance . However , we can not at present conclude that any of these are associated with a pulsar in SNR 1987A . As a check on the system , we also observed PSR B0540 - 69 , a young pulsar which also lies in the LMC . We found eight giant pulses at the DM of this pulsar . We discuss the implications of these results for models of the supernova remnant , neutron star formation and pulsar evolution .