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While non-coding G-quadruplexes (G4s) act as conserved regulatory elements when located in gene promoters and splice sites, the evolutionary conservation of G4s in protein-coding regions remains under-explored. To address the evolutionary dynamics acting on coding G4s, we mapped and characterized potential G4-forming sequences (PGQS) across the orthologous coding DNA sequences (CDS) of twenty-two primates. We found that the PGQS count correlated with the number of available orthologs and, to a lesser extent, with phylogenetic distance from humans. PGQS motifs showed high co-localization, especially among closely related species. Thermodynamic stability, inferred from the minimum folding free energy, emerged as an important factor associated with evolutionary patterns: low stability PGQSs (minimum folding free energy ≥ –10 kcal/mol) were more conserved, whereas high stability PGQSs (minimum folding free energy ≤ –30 kcal/mol) showed reduced conservation, although both categories remained more conserved than the CDS baseline. Consistently, indel scores were negatively correlated with the minimum folding free energy of PGQSs, suggesting an association between stable motifs and insertion or deletion events. In line with this, G-rich tandem repeats exhibited elevated indel mutagenesis, consistent with their propensity to fold into highly stable G4s. Altogether, these findings reveal that PGQSs simultaneously act as conserved elements and sources of structural instability, reflecting antagonistic selective pressures that preserve sequence function while generating instability through structure formation.