Juedeman was born in the community with the unlikely name of Slick in Creek County in east central Oklahoma. He served three terms from 1953 to 1959 in the Montana House of Representatives, based in the capital city of Helena. For a time he was the House Majority Leader. He was also Montana state Republican Party chairman. In 1958, he moved to Odessa in Ector County in West Texas to enter the oil and natural gas business with his brother-in-law, Morris Ford "Jake" Lawless (1903-1986). Within the next several years, Juedeman became the spiritual founder of the Permian Basin division of the Texas GOP and did not always receive proper recognition for his role as the original “Mr. Republican” of Ector County. In Juedeman’s obituary in the Odessa American, the paragraph on politics describes him as a “mainstay” of the Texas Republican Party, one “instrumental in building an effective party apparatus in Ector County during the early 1960s, an era when state and local politics [was] dominated by the Democratic Party. Relying on his experience ... in Montana politics, Juedeman mentored young Republican candidates running for office, advised the party faithful on the creation of an effective vote-getting organization, and campaigned tirelessly for Texas Republican issues and candidates for over three decades. Characterized by a positive attitude and an ever-present sense of humor, he zestfully entered the political fray. Victories were received with cheerful grace, and losses . . . without bitterness or rancor.”
Previously a wheat farmer in Toole County, Montana, near the Canadian border, Juedeman had no trouble adjusting to Odessa. He became active in many civic causes: the Chamber of Commerce and the boards of both Odessa College and the University of Texas of the Permian Basin.
Texas political activities
Juedeman was credited with helping in 1962 to elect Ed Foreman, then of Odessa, a millionaire at twenty-six and later a motivational speaker in Dallas, to Texas's 16th congressional district the lines of which stretched from El Paso to the Permian Basin. After a single term in the House in which was punched in the face in 1963, after having called the Democrat Henry B. Gonzalez of San Antonio, “a pinko,” Ed Foreman was unseated during the Johnson-Humphrey landslide in Texas in 1964 by the Democrat Richard Crawford White of El Paso. In 1968, Foreman returned for another single term to Congress from a district in his native southeastern New Mexico.
Texas State Representative George E. “Buddy” West of Odessa,  who worked to procure the Presidential Museum and Leadership Library on the UTPB campus, said that Juedeman was his mentor too: “He’s always been to me ‘Mr. Republican’ in Ector County. He was a Republican when Republican wasn’t cool.”
Gary Johnson, former Ector County Republican chairman, recalls that Juedeman was "always willing to do what nobody could if somebody asked him. He wouldn't want to interfere or force his way, but if you went to him for an opinion on something or for help, he would do what he could." Bill Elms, a businessman and Republican former member of the Ector County Commission, refers to Juedeman’s “political knack . . . that was helpful to us. Back then, the Republican would maybe have only one thousand votes in our primary. We were just getting started, and he had no other objective than to help us out.”
Death and legacy
Juedeman died at the age of ninety-five in the Odessa Medical Center, of which he was also a board member. He was active in the First Baptist Church of Odessa. He was predeceased by his wife, Ithai M. Juedeman (1908-1988). The couple is interred at Sunset Memorial Gardens in Odessa. His survivors included a daughter, Dr. Lynne J. Baldwin (born 1946) of Omaha, Nebraska, and a brother, Ralph E. Juedeman (1917-2010) of Bristow, Oklahoma.
On Juedeman’s death, Jim Reese, the mayor of Odessa from 1968 to 1974 and two-time candidate for Texas's 19th congressional district seat, told the Odessa American: "He was active in Republican Party activities out here when you could fit us all in a phone booth. . . . He was a very, very energetic guy . . . a likeable fellow. His sense of humor was one thing I remember about him. Regardless how things went in a campaign – win or lose – he always had that sense of humor."Juedeman had even tried to draft Reese into seeking the 1972 Republican gubernatorial nomination, but the selection instead went to then State Senator Henry C. Grover of Houston, who was defeated in a heavily contested election by the Democrat Dolph Briscoe of Uvalde, Texas.
- Social Security Death Index
- Rudy Juedeman obituary, Odessa American, January 21, 2004
- Billy Hathorn, "Mayor Jim Reese of Odessa and the Republican Party in the Permian Basin", The West Texas Historical Association Year Book, Vol. LXXXVII (October 2011), p. 145
- “The Eternal Challenger,” Texas Monthly (October 1972), 176; the initial election of Henry B. Gonzalez (1916-2000) to the U.S. House came in a special election held on November 4, 1961, when Gonzalez was a state senator. This was the last political event known to Speaker of the United States House of Representatives Sam Rayburn, who died twelve days later.
- Foreman, Edgar Franklin (born 1933) and White, Richard (1923-1998), Biographical Directory of the United States Congress, 1974-Present, Website: bioguide.congress.gov, Access date=April 9, 2012
- George West (1936-2008) was unseated in the Republican primary election shortly before his death by Tryon D. Lewis (born 1947), a former judge, who still holds the Odessa-based seat in the Texas House of Representatives.
- Aaron Bensonhaver, “The Presidential Museum Has a New Home,” Odessa American, August 19, 2002
- Reese, p. 145
- David J. Lee, “Friends fondly remember ‘Mr. Republican’,” ‘’Odessa American’’, January 22, 2004, 1B-2B.
- Reese, pp. 145-146
- Reese, pp. 143-144