He is the son of Roderick Burgess, mother unknown (but probably Ethel Cripps). He is taught by his father, and takes part in his rituals. On Roderick Burgess' death, Alex inherits his estate, including his magical order. He keeps Morpheus imprisoned, like his father trying to bargain for power and immortality in exchange for his releases. The order enjoys a resurgence in popularity in the 1960s, but by the 1970s it declines again. Alex passes the order to his boyfriend, Paul McGuire (formerly a gardener at the estate), and becomes obsessed with his prisoner and with his father. Finally, in 1988, Morpheus' guards fall asleep, and Morpheus escapes. He puts Alex into a nightmare of 'eternal waking'; he is forever dreaming he is waking up, and each waking degenerates into another horrible nightmare. This nightmare ends only with Morpheus' death in the ninth collection of issues in the series, The Kindly Ones.
Alex is quite tall and short-sighted. He has brown hair which he wears in a variety of styles throughout his life, but by old age he is bald and has come to resemble his father very closely. His relationship with McGuire is deep and heartfelt, but his obsessions with his father and with Morpheus eventually come to rule his life.