Alfio Galigani was born in Perugia on October 1, 1924, and began studying music at nine at the city's Liceo Musicale Comunale (the institution that later became the Conservatorio "Francesco Morlacchi"). He went on to earn a clarinet diploma from the Cosenza Conservatory and a saxophone diploma from the Bologna Conservatory, and started performing professionally at 16 in light-music orchestras. From 1946 he worked across classical, jazz and light-music settings at once, including a run as tenor-sax soloist with the Radio Roma orchestra that same year.

His account of the years that followed, given in a 2001 interview published by jazzitalia.net, traces a working Italian reed player's path through the postwar decades: a stint with Maurice Chevalier's orchestra at the Maxim in Cannes in the summer of 1949; a jazz quintet of his own, Hot Gatto Nero, that ran through the early-to-mid 1950s with saxophonist Riccardo Laudenzi as a member for four or five years; and a nightly three-month run at Palermo's Villa Igea in 1953 alongside violinist Stéphane Grappelli, reed player Umberto Cesari, Laudenzi and drummer Brando Trequattrini, which Galigani himself remembered as "an orgy of jazz every night for about three months." On May 30, 1953, he played what he called a memorable concert at the Perugia Conservatory alongside Cesari, Laudenzi, bassist Pepito Pignatelli and singer Lilian Terry.

Composer and RAI arranger Gino Marinacci, whom Galigani had worked with in a Garinei and Giovannini theatrical production in the mid-1950s, brought him into RAI's orbit with Armando Trovajoli's orchestra; Galigani held a chair in RAI-TV orchestras from 1958 to 1978, with a run at Rome's Teatro dell'Opera in 1965. Inside that twenty-year studio career came the jazz engagement he recalled most fondly next to the Grappelli residency: in the summer of 1968, playing in an orchestra drawn from Rome's best professional jazz musicians for a tour with Lionel Hampton, who "used me continuously as clarinet soloist alongside him, whether he was playing the vibraphone or had sat down at the drums." The same year, Galigani recorded as alto-sax soloist on "Saxologia," a piece for saxophone quartet and guitar written by fellow reedist Eraclio Sallustio, released on the various-artists LP Natura e Musica N. 1 (1968, Grand Prix) alongside Baldo Maestri, Sallustio and baritone player Antonio Russo — the same players, with Galigani on alto, who made up the Italian Saxophone Quartet (Quartetto di Saxofoni Italiano), which he belonged to in its later years. His RAI-era studio work also produced session credits, confirmed via the Discogs API, on Piero Umiliani's orchestral LP Fischiando in Beat (1970) and, per an independent collector's account, on Umiliani's "Risaie" from the album Paesaggi (1971, credited to Suonano I Mark 4), on which he is named as the featured flute.

In 1972 he played flute, alto flute and bass saxophone on Atom Flower's, a Gino Marinacci LP recorded at Piero Umiliani's Sound Work Shop studio and released on the Roman Record Company label — a record that has since become a cult item among Italian library-and-jazz-funk collectors and been reissued repeatedly (Mono Jazz/Right Tempo, 2024, among others), with Marinacci himself billed on its original sleeve as winner of the 1971 Venice festival's Premio Louis Armstrong for best Italian jazzman. An undated 7" EP on the small Sonic label, Holiday for Two — four Miro Graziani compositions credited to "Complesso diretto da Alfio Galigani" ("ensemble directed by Alfio Galigani") — is, per the Discogs contributor who catalogued it, probably the only 45 ever released under his own direction; Discogs tags its style as Hard Bop and Modal.

Galigani's most lasting institutional legacy began on December 30, 1973, when he directed the first concert of the newly formed Perugia Big Band at the Sala dei Notari in Perugia's Palazzo dei Priori, succeeding Miro Graziani as the band's director and, in his own words, bringing "this orchestra of amateurs to a semi-professional level." The following July, he led the Perugia Big Band to Umbria Jazz 1974, playing dates in both Perugia and Todi; on July 28, 1974, in Todi's Piazza del Popolo, the band shared the evening's bill with the Thad Jones Sextet and Charles Mingus, representing the domestic side of that year's festival lineup alongside Mario Schiano's quintet. In 1977 the Perugia Big Band, with Galigani conducting, recorded "Rapsodia Americana," a Miro Graziani composition and arrangement, on a promotional-only 7" for the Mirage/Redar Hi-Fi labels.

Galigani began teaching clarinet at the Perugia Conservatory in 1974 and was given the saxophone chair there in 1975-76, a post he held until retiring from teaching in 1981; ilsaxofonoitaliano.it, a reference site for the history of the instrument in Italy, credits him as one of the historical founders of saxophone teaching in Italian conservatories. Alongside his conservatory classes he founded the Orchestra della Charlie Parker Jazz School, teaching sixteen students the vocabulary of jazz phrasing and, in his words, "the essence of swing, Count Basie style." Saxophonists Roberto Todini and Francesco Santucci both took their conservatory diplomas under him; saxophonist Rino Cirinnà, later a Berklee student and collaborator of Massimo Urbani and Sandro Satta, also studied privately with Galigani, in Rome.

On June 24, 1982, Galigani suffered sudden bilateral sensorineural hearing loss, attributed to decades of wearing headphones during RAI recording sessions, which ended his performing career; he continued to improvise privately. He died in Rome on July 7, 2010, survived by his wife Vincenza and daughters Giannetta and Daniela.

Galigani's own account of his career places its emotional peaks in ensemble jazz work alongside visiting American stars — the 1953 Grappelli residency in Palermo and the 1968 Lionel Hampton tour, where he played featured clarinet obbligato lines around Hampton's vibraphone and drums — rather than in any recording under his own name. His teaching, by his own description, centered on swing-era vocabulary "alla Count Basie," and it is as a big-band leader that he left his clearest institutional mark: the Perugia Big Band, which he directed from its founding concert in December 1973 through its 1974 Umbria Jazz appearances and into the back half of the decade. His handful of studio-session jazz credits — a saxophone-quartet recording, a jazz-funk-adjacent library LP for Gino Marinacci, and an obscure 7" EP tagged Hard Bop on Discogs — reflect the working reality of a Rome-based studio multi-reedist of the 1960s-70s more than a leader's discography, and are treated here as exactly that: real, but incidental to a career built on bandstands and classrooms rather than record labels.