  We find all Ricci semi-symmetric as well as all conformally semi-symmetric
spacetimes. Neither of these properties implies the other. We verify that only
conformally flat spacetimes can be Ricci semi-symmetric without being
conformally semi-symmetric and show that only vacuum spacetimes and spacetimes
with just a $\Lambda$-term can be Ricci semi-symmetric without being
conformally semi-symmetric.
