This protocol describes the directed evolution of artificial endonuclease and ligase enzymes composed of synthetic genetic polymers (XNAzymes), using 'cross-chemistry selective enrichment by exponential amplification' (X-SELEX). The protocol is analogous to (deoxy)ribozyme selections, but it enables the development of fully substituted catalysts. X-SELEX is initiated by the synthesis of diverse repertoires (here 10(14) different sequences), using xeno nucleic acid (XNA) polymerases, on DNA templates primed with DNA, RNA or XNA oligonucleotides that double as substrates, allowing selection for XNA-catalyzed cleavage or ligation. XNAzymes are reverse-transcribed into cDNA using XNA-dependent DNA polymerases, and then PCR-amplified to generate templates for subsequent rounds or deep sequencing. We describe methods developed for four XNA chemistries, arabino nucleic acids (ANAs), 2'-fluoroarabino nucleic acids (FANAs), hexitol nucleic acids (HNAs) and cyclohexene nucleic acids (CeNAs), which require ∼1 week per round, and typically 10-20 rounds; in principle, these methods are scalable and applicable to a wide range of novel XNAzyme chemistries, substrates and reactions.