CBASS and Pycsar are anti-phage defense systems in diverse bacteria that use cyclic nucleotide signals to induce cell death and prevent viral propagation1,2. Phages use multiple strategies to defeat host CRISPR and restriction-modification systems3–10, but no mechanisms are known to evade CBASS and Pycsar immunity. Here we show that phages encode anti-CBASS (Acb) and anti-Pycsar (Apyc) proteins that counteract defense by specifically degrading cyclic nucleotide signals that activate host immunity. Using a biochemical screen of 57 phages in E. coli and B. subtilis, we discover Acb1 from phage T4 and Apyc1 from phage SBSphiJ as founding members of distinct families of immune evasion proteins. Crystal structures of Acb1 in complex with 3′3′-cGAMP define a mechanism of metal-independent hydrolysis 3′ of adenosine bases, enabling broad recognition and degradation of cyclic di- and trinucleotide CBASS signals. Structures of Apyc1 reveal a metal-dependent cNMP phosphodiesterase that uses relaxed specificity to target Pycsar cyclic pyrimidine mononucleotide signals. We show that Acb1 and Apyc1 block downstream effector activation and protect from CBASS and Pycsar defense in vivo. Active Acb1 and Apyc1 enzymes are conserved in phylogenetically diverse phages, demonstrating cleavage of host cyclic nucleotide signals is a key strategy of immune evasion in phage biology.