G-quadruplex is a four-stranded G-rich DNA structure that is highly susceptible to oxidation. Despite the important roles that G-quadruplexes play in telomere biology and gene transcription, neither the impact of guanine lesions on the stability of quadruplexes nor their repair are well understood. Here, we show that the oxidized guanine lesions 8-oxo-7,8-dihydroguanine (8-oxoG), guanidinohydantoin (Gh) and spiroiminodihydantoin (Sp) reduce the thermostability and alter the folding of telomeric quadruplexes in a location-dependent manner. Also, the NEIL1 and NEIL3 DNA glycosylases can remove hydantoin lesions but none of the glycosylases, including OGG1, are able to remove 8-oxoG from telomeric quadruplexes. Interestingly, a hydantoin lesion at the site most prone to oxidation in quadruplex DNA is not efficiently removed by NEIL1 or NEIL3. However, NEIL1, NEIL2 and NEIL3 remove hydantoins from telomeric quadruplexes formed by five TTAGGG repeats much more rapidly than the commonly studied four-repeat quadruplex structures. We also show that APE1 cleaves furan in selected positions in Na⁺-coordinated telomeric quadruplexes. In promoter G-quadruplex DNA, the NEIL glycosylases primarily remove Gh from Na⁺-coordinated antiparallel quadruplexes but not K⁺-coordinated parallel quadruplexes containing VEGF or c-MYC promoter sequences. Thus, the NEIL DNA glycosylases may be involved in both telomere maintenance and in gene regulation.