The first round in the local elections, held last Sunday, May 18, reveal a significant growth of parties to the left of SYRIZA, in particular the KKE, but also a shift to the right within the right-wing camp, with Golden Dawn picking up votes. What we have is a sharpening of the class polarisation within Greek society, a harbinger of renewed class conflict in the coming period. Here we provide an analysis by a Greek Marxist of the results of the first round.