The Apellai (Ancient Greek: ἀπέλλαι), was an ancient annual family-festival of the Northwest Greeks, at least at Delphi, similar to the Ionian Apaturia. The festival was apparently spread by the Dorians as inferred by the use of the month name Apellaios in various Dorian localities. Sacrificial animals, called apellaia, seem to have been offered at the Apellai on the occasion of a youth becoming an adult. It is thought to have been a festival of Apollo.

The word apellai occurs only in the plural, with all known uses of the word coming from Doric speaking regions of Greece. It occurs in the Labyad inscription (late fifth to fourth century BC) of Delphi, as well as two first-century BC inscriptions from Sparta's seaport town of Gytheion.

Hesychius explains the meaning of the word apellai with the gloss: sekoi, ekklesiai, archairesiai. The word sekos (plural sekoi) can refer to various kinds of enclosures, while ekklesiai refers to official public assemblies, and archairesiai refers, more specifically, to public assemblies for the election of magistrates. In light of Heschius's explanation of the apellai in terms of such assemblies, Heschius's sekoi might be interpreted as referring to either the entire enclosure within which such assemblies were held, or the subdivisions of such assemblies into precincts (e.g. voting precincts). The derived denominal verb infinitive apellazein (ἀπελλάζειν) occurs in the Lycurgean Great Rhetra (c. 700 BC) of Sparta, which Plutarch explains as meaning the same as ekklesiazein (ἐκκλησιάζειν) 'to conduct an assembly'.

The use of the word in the two first-century BC inscriptions from Gytheion help confirm the explanations given by Hesychius and Plutarch. Both inscriptions contain the formulaic expression used to introduce official decrees of the people's assembly: "ἔδοξε τῶι δάμωι" ('it was decided by the people'), followed by: "ἐν ταῖς μεγάλαις ἀπελλαῖς" ('at the great apellai'). From this it has been inferred that, at Sparta, there were also 'lesser apellai'. Wade-Gery further suggested the possibility that, the Spartan 'great apellai' was held annually, while 'lesser apellai' were held monthly.

The etymology of the word apellai is unknown. According to Robert Beekes, "a connection with IE *h₂pel- would be the most easy solution, but there are no obvious cognates for such a root." Another Hesychius gloss explains the (related?) word apellein with the word apokleiein, a form of the verb apokleio (ἀποκλειω) that means 'shut out', 'close', 'shut away'. According to Beekes this "may well provide the original meaning of ἀπέλλαι, 'enclosed space, meeting place'."

The only explicit mention of a festival called the Apellai occurs in the Labyad inscription, which records the law of the Ladyadai, a familial group at Delphi assumed to be similar to an Ionian phratry. The first month of the Delphic calendar was called Apellaios (Ἀπελλαῖος), and the inscription mentions an Apellai festival at Delphi held during that month at which the Labyaidai feasted. The inscription regulates the procedures for admission of members into the Ladyadai (as overseen by certain officials called the tagoi), which required the formal approval, of both the entire Ladyadai, and the particular subgroup (patria) to which the new member would belong, and which seem to have involved three points of admission, marriage, the birth of a (probably male) child, and passage into adulthood.

In particular, the inscription regulates the "offerings of sacrificial victims and of cakes". The "sacrificial victims" were animal sacrifices called apellaia (ἀπελλαῖα), which are to be brought and received only on the day of the Apellai, and the inscription prescribes that if the presiding Labyad officials (tagoi) were to "receive them on a day other than the Apellai, each of them is to pay a fine of 10 drachmas", while the cake offerings (called daratai) were to be made by Ladyadai "on the occasion of marriages or children". From this it has been concluded that the Apellai were the Delphic equivalent of the Ionian festival of the Apaturia, at which the formal admission of new adult members of a phratry occurred.

The Apellai, as the name of a festival, is only attested for Delphi, however the month name Apellaios was widespread among the Dorians, from which it has been inferred that the Apellai was also widespread. In addition to Delphi, localities where the month name Apellaios is attested include, in Central Greece, Ozolian Locrian Chaleion, Oianthea, and Tolophon, and Phthiotic Lamia and Oitaia, in the Peloponnese, Argos and Epidaurus, the island of Tenos in the Aegean, Olus on Crete, Heraclea in the Lucanian region of Southern Italy, Tauromenion in Sicily, and Bithynian Chalcedon in Anatolia.