Baxter joined his first band at age 11. While still a high school student, he worked at Manny’s Music Shop in Manhattan in 1966. At Manny’s, Baxter met guitarist Jimi Hendrix, who was just beginning his career as a frontman. For a short period during that year, Baxter was the bassist in a Hendrix-led band called Jimmy James and the Blue Flames, along with fellow Manny’s employee Randy California. Moving to Boston to attend college, Baxter worked as a guitar technician and amplifier repairman at Jack’s Drum Shop on Boylston Street.

Baxter graduated from the Taft School in 1967 in Watertown, Connecticut, and was a self-described preppie. At Taft, he played drums in an upperclassmen band, King Thunder and the Lightning Bolts. He enrolled at the School of Public Communication (now College of Communication) at Boston University in September 1967, where he studied journalism while continuing to perform with local bands.

Baxter first reached a wide rock audience in 1968 as a member of the psychedelic rock band Ultimate Spinach. Baxter joined the band for Ultimate Spinach III, their third and final album. After leaving the band, he played with the Holy Modal Rounders and backed singer Buzzy Linhart. By this time, he was using the moniker “Skunk,” although the nickname’s origins have been kept secret by Baxter.

After the breakup of Ultimate Spinach, Baxter relocated to Los Angeles, finding work as a session guitarist. In 1972 he became a founding member of the band Steely Dan, along with guitarist Denny Dias, guitarist-bassist Walter Becker, keyboardist-vocalist Donald Fagen, drummer Jim Hodder and vocalist David Palmer.

Baxter appeared with Steely Dan on their first three albums, Can’t Buy a Thrill in 1972, Countdown to Ecstasy in 1973, and Pretzel Logic in 1974. He contributed the guitar fills and signature solo heard on the group’s highest charting hit “Rikki Don’t Lose That Number.”

While finishing work on Pretzel Logic, Baxter became aware of Becker and Fagen’s intentions to retire Steely Dan from touring and work almost exclusively with session players. With that in mind, Baxter left the band in 1974 to join The Doobie Brothers, who at the time were touring in support of their fourth album What Were Once Vices Are Now Habits. As a session man, he had contributed pedal steel guitar on Vices as well as “South City Midnight Lady” on its predecessor, The Captain and Me. Baxter’s first album as a full member of the group was 1975’s Stampede. He contributed an acoustic interlude (“Precis”), significant turns on slide and pedal steel guitar, and the guitar solo for the hit single “Take Me in Your Arms (Rock Me A Little While)”.

In early 1979, Baxter and co-founding drummer John Hartman left the band.

In 1982, he featured on Spirit’s album Spirit of ’84, released as The Thirteenth Dream outside of the USA.

In 1984, Baxter played keyboards with Bobby and the Midnites’ Bob Weir, Billy Cobham, Bobby Cochran, Kenny Gradney (“Tigger”), and Dave Garland at the Capitol Theatre in Passaic, New Jersey. That same year, he produced and played guitar and synthesizer on the band’s album Where the Beat Meets the Street on Columbia Records.

In 1986, Baxter joined James Brown and Maceo Parker on guitar for several North American tour dates.

In 1990, Baxter joined John Entwistle, Joe Walsh, Keith Emerson, Simon Phillips and relatively unknown vocalist Rick Livingstone in a supergroup called The Best. The group released a live performance video in Japan before disbanding. He also produced two albums for the hard rock band Nazareth, and also produced albums for Carl Wilson, Livingston Taylor, The Ventures, and Nils Lofgren. He was producer on the 1982 Bob Welch album Eye Contact. In 1991 Baxter also produced a documentary video, “Guitar” (Warner Brothers VHS and LaserDisc), in which he travels the world and interviews guitarists he admires. In 1994 he performed on the video game Tuneland.

Backed by several influential Capitol Hill lawmakers, Baxter received a series of security clearances so he could work with classified information. In 1995, Pennsylvania Republican Congressman Curt Weldon, then the chairman of the House Military Research and Development Subcommittee, nominated Baxter to chair the Civilian Advisory Board for Ballistic Missile Defense.

In 1997 Baxter scored the movie The Curse of Inferno.

Baxter worked on the animated TV series King of the Hill in 1997, composing songs for three episodes: “Peggy the Boggle Champ”, “Hank’s Unmentionables Problem”, and “Square Peg”. Also in 1997, he worked on two other TV series as a composer: The Blues Brothers Animated Series and The Curse of Inferno. He composed for Shelley Duvall’s Bedtime Stories TV series episode “Bootsie Barker Bites/Ruby the Copycat” in 1993, the Pee-wee’s Playhouse episode “Tons of Fun” in 1987, and the Beverly Hills, 90210 episode “The Green Room” in 1990. He is credited on the movie soundtrack for the feature film Roxanne (1987) as writer and producer for the songs “Party Tonight” and “Can This Be Love”. Other credits include music for Class of 1984 (1982): “You Better Not Step Out of Line” and as a performer on “Suburbanite”. He appeared in the film Blues Brothers 2000 and can be heard on the cast album.

In 2000, Baxter considered challenging Representative Brad Sherman for the 24th Congressional District seat in California before deciding not to run because the district which is where he lives is Democratic and Baxter would have lost by a landslide.

In April 2005, he joined the NASA Exploration Systems Advisory Committee.

Baxter was a member of an independent study group that produced the Civil Applications Committee Blue Ribbon Study recommending an increased domestic role for US spy satellites in September 2005. This study was first reported by The Wall Street Journal on August 15, 2007. He is listed as “Senior Thinker and Raconteur” at the Florida Institute for Human and Machine Cognition, and is a Senior Fellow and Member of the Board of Regents at the Potomac Institute for Policy Studies.

Baxter continues to do studio work, most recently on tribute albums to Pink Floyd and Aerosmith. In 2012, he appeared on keyboardist Brian Auger’s Language of the Heart, and The Beach Boys’ That’s Why God Made the Radio. He also occasionally plays in The Coalition of the Willing, a band comprising Andras Simonyi, Hungarian Ambassador to the United States; Alexander Vershbow, US Ambassador to South Korea; Daniel Poneman, formerly of the United States National Security Council and later the Obama Administration’s Deputy Secretary of Energy; and Lincoln Bloomfield, former United States Assistant Secretary of State for Political-Military Affairs. On June 19, 2007, Baxter jammed with former White House Press Secretary Tony Snow’s band Beats Workin’ at the Congressional Picnic held on the White House South Lawn.