There are two fanzines which were named Fanac, one primarily a newszine published by Ron Ellik and Terry Carr in the late 50s and early 60s, and the other published by Swedish fan John-Henri Holmberg from 1963 to 1994.
Fanac by Terry Carr and Ron Ellik
Fanac was a news-and-chatterzine published by Terry Carr and Ron Ellik, begun in 1958, in the midst of (true) Seventh Fandom. Its activity promoted the 1958 Worldcon (SoLaCon), and gave wide circulation to the series of pro and fan deaths in 1958, on which it bestowed the title of The Year of the Jackpot (in reference to the Heinlein story of that title).
It started as a weekly, but moved to biweekly, with issues typically being four pages. (The February 1960 issue was an exception. It was a second anniversary issue, titled Fannish II and ran over forty pages, including a thirty-page section summarizing the 1959 Fanac Poll and an index to Fanac's first two years. The cover of this issue was a photo of a local fan, Trina Castillo, dressed in only a propeller beanie and a copy of Fancyclopedia II.)
Besides news, it had features such as Walt Willis's column P*L*I*N*T*H, about happenings in Irish Fandom. It won the 1959 Best Fanzine Hugo.
In September 1960 Ron Ellik quit as co-editor and was replaced by Miriam Carr. In 1961, the Carrs let it lapse into hiatus and it was revived by Walter Breen, but he was unable to keep to the schedule.
Fanac by John-Henri Holmberg
Holmberg published the Swedish newszine Fanac, which was modeled and named after Carr and Ellik Fanac beginning in late 1963. This was near the end of the run of SF-Times which helped to maintain source of news for Swedish fans throughout the decade. Holmberg used the pseudonym Carl Brandon, Jr. in early issues, after the hoax fan invented by Fanac co-editor Terry Carr (and others) in the mid 50s. As Holmberg later remembered, "I wasn't particularly inspired by Willis or Irish Fandom, but instead was totally fascinated by the fannish Berkeley and later New York group, including Terry Carr, Ted White, Ron Ellik, Dave Rike, Boob Stewart, and Carl Brandon, Sr."
Holmberg's Fanac lasted until 1982, a total of 117 issues. He re-launched it in mid-1990s, but it went dormant after only two issues
See Fanac for other meanings of the word.