He was born sometime in the mid-fourth century on an island in the Aegean. For a time he lived successfully in the world, receiving a good education in Constantinople, then serving for a time for the Prefect of the Praetorium. But, becoming aware of the vanity of worldly things, he answered Christ's call, gave away all his goods to the poor and entered a monastery in Syria. After four years in obedience, he came to feel that the security of monastic life was inconsistent with the Gospel command to take no thought for the morrow; so he withdrew to the desert, taking with him only his garment and the Book of the Gospel. There he lived alone for seven years.
  At the end of this period he set out on an apostolic mission to Mesopotamia, where he brought many to Christ: the city prefect Rabbula was converted after Alexander brought down fire from heaven, and a band of brigands who accosted the Saint on the road were transformed into a monastic community. He finally fled the city when the Christians there rose up demanding that he be made bishop. He once again took up a solitary life in the desert beyond the Euphrates, spending the day in prayer and part of the night sheltered in a barrel. There he remained for forty years. His holiness gradually attracted more than four hundred disciples, whom Alexander organized into a monastic community. Each disciple owned only one tunic, and was required to give away anything that they did not need for that day. Despite this threadbare life, the monastery was able to set up and run a hospice for the poor!
  Alexander was perplexed as to how the admonition Pray without ceasing (1 Thess. 5:17) could be fulfilled by frail human flesh, but after three years of fasting and prayer, God showed him a method. He organized his monks into four groups according to whether their native language was Greek, Latin, Syriac or Coptic, and the groups prayed in shifts throughout the day and night. Twenty-four divine services were appointed each day, and the monks would chant from the Psalter between services. The community henceforth came to be known as the Akoimetoi, the Unsleeping Ones. (Similar communities later sprang up in the West, practicing what was there called Laus Perennis; St Columban founded many of these.)
  Always desiring to spread the holy Gospel, Saint Alexander sent companies of missionaries to the pagans of southern Egypt. He and a company of 150 disciples set out as a kind of traveling monastery, living entirely on the charity of the villages they visited. Eventually they settled in some abandoned baths in Antioch, setting up a there a monastery dedicated to the unceasing praise of God; but a jealous bishop drove them from the city. Making his way to Constantinople, he settled there with four monks. In a few days, more than four hundred monks had left their monasteries to join his community. The Saint organized them into three companies — Greeks, Latins and Syrians — and restored the program of unsleeping prayer that his community had practiced in Mesopotamia. Not surprisingly, his success aroused the envy and anger of the abbots whose monasteries had been nearly emptied; they managed to have him condemned as a Messalian at a council held in 426. (The Messalians were an over-spiritualizing sect who believed that the Christian life consisted exclusively of prayer.) Alexander was sent back to Syria, and most of his monks were imprisoned; but as soon as they were released, most fled the city to join him again. The Saint spent his last years traveling from place to place, founding monasteries, often persecuted, until he reposed in 430, 'to join the Angelic choirs which he had so well imitated on earth.' (Synaxarion)
  The practice of unceasing praise, established by St Alexander, spread throughout the Empire. The Monastery of the Akoimetoi, founded by a St Marcellus, a successor of Alexander, was established in Constantinople and became a beacon to the Christian world. 'Even though it has not been retained in today's practice, the unceasing praise established by Saint Alexander was influential in the formation of the daily cycle of liturgical offices in the East and even more so in the West.' (Synaxarion)