In many animals, establishment of the germ line depends on segregation of a specialized cytoplasm, or 'germ plasm', to a small number of germline precursor cells during early embryogenesis. Germ plasm asymmetry involves targeting of RNAs and proteins to a specific region of the oocyte and/or embryo. Here we demonstrate that germ plasm asymmetry also depends on degradation of germline proteins in non-germline (somatic) cells. We show that five CCCH finger proteins, components of the Caenorhabditis elegans germ plasm, are targeted for degradation by the novel CCCH-finger-binding protein ZIF-1. ZIF-1 is a SOCS-box protein that interacts with the E3 ubiquitin ligase subunit elongin C. Elongin C, the cullin CUL-2, the ring finger protein RBX-1 and the E2 ubiquitin conjugation enzyme UBC5 (also known as LET-70) are all required in vivo for CCCH finger protein degradation. Degradation is activated in somatic cells by the redundant CCCH finger proteins MEX-5 and MEX-6, which are counteracted in the germ line by the PAR-1 kinase. We propose that segregation of the germ plasm involves both stabilization of germline proteins in the germ line and cullin-dependent degradation in the soma.