Centrioles are composed of long-lived microtubules arranged in nine triplets. However, the contribution of triplet microtubules to mammalian centriole formation and stability is unknown. Little is known of the mechanism of triplet microtubule formation, but experiments in unicellular eukaryotes indicate that delta-tubulin and epsilon-tubulin, two less-studied tubulin family members, are required. Here, we report that centrioles in delta-tubulin and epsilon-tubulin null mutant human cells lack triplet microtubules and fail to undergo centriole maturation. These aberrant centrioles are formed de novo each cell cycle, but are unstable and do not persist to the next cell cycle, leading to a futile cycle of centriole formation and disintegration. Disintegration can be suppressed by paclitaxel treatment. Delta-tubulin and epsilon-tubulin physically interact, indicating that these tubulins act together to maintain triplet microtubules and that these are necessary for inheritance of centrioles from one cell cycle to the next.