ENGLEWOOD, Colo. -- Having just completed their first back-to-back losing seasons since the early 1970s, the Denver Broncos fired Vance Joseph on Monday, a day after the team finished 6-10.

Joseph, who had two years remaining on the four-year deal he signed in 2017, lasted just 32 games with the team. The Broncos now will search for the fourth head coach in John Elway's seven-year tenure as the team's top football executive.

"I spoke with Vance this morning and thanked him for all of his hard work as our head coach," Elway said via a statement. "Although we decided to make this change, I believe Vance is a good football coach who has a bright future in this league.

"Vance made a lot of strides and deserves credit for how hard and competitively the team played this season. There's always going to be a high standard here -- the bottom line is we need to win more football games. We're excited about the foundation that's being built and look forward to putting in the work to get the Broncos back on the winning track."

Earlier Monday, Joseph told ESPN's Josina Anderson, "I want to be the head coach of this team. I would like to get the third year. I think two years is just too short to judge a coach and a team."

It was a bumpy ride for Joseph, who played and coached at the University of Colorado before he began his NFL coaching career. He faced an almost constant wave of criticism for the team's offense and its quarterback play. The Broncos finished 5-11 in his first year and missed the playoffs in both of his seasons as head coach. It was the first time the Broncos finished consecutive seasons with a losing record since 1971 and 1972.

Since Elway became Broncos GM in 2011, John Fox coached the first four seasons, and Gary Kubiak handled two seasons -- including the Super Bowl 50 win -- before stepping down due to health concerns. Joseph replaced him.

When he was hired, Joseph called the opportunity "a dream job" and said the Broncos "have an unbelievable winning tradition ... but what makes this even more special is it's a place ready to win. This is not a rebuilding situation -- it is a reboot."

Vance Joseph was 11-21 during his two seasons as head coach of the Broncos. Kyle Terada/USA TODAY Sports

And with a nod to the future, Joseph said on his first day on the job that "the standards around here won't change -- those are to win championships."

Joseph's teams did work hard and consistently had the public support of the Broncos' highest-profile players like linebacker Von Miller and cornerback Chris Harris Jr. This past season the Broncos pushed some of the league's best teams to the limit with losses to the Kansas City Chiefs (twice), the Los Angeles Rams and Houston Texans by a combined 16 points.

The Broncos were in position to win at least three of those games before their own mistakes and decision-making did them in, including letting a 10-point fourth-quarter lead slip away against the Chiefs in Denver and missing a 51-yard field goal on the last play of the loss to the Texans.

Overall, the Broncos consistently struggled with penalties, usually at key moments in their games, as well as what Harris called "high school mess-ups" on the field. Joseph's teams also won only four road games in his two seasons. The Broncos also stumbled after quality starts in both years, having started the 2017 season at 3-1 before an eight-game losing streak, and they opened this season at 2-0 before a four-game losing streak.

But Joseph also was a victim of the roster, at least sometimes, especially as the Broncos continued to search for a long-term answer at quarterback; the quarterback carousel has seen four different players start over the past 32 games. None of the five quarterbacks the Broncos have selected in the draft during Elway's tenure is on the roster or practice squad.

The miss on quarterback Paxton Lynch, a player Elway traded up in the first round to select in the 2016 draft, was significant. It also put the Broncos in a search for a quarterback that resulted in three different quarterbacks starting games in 2017, leading to Case Keenum's signing in March.

Lynch isn't even a prospect for the Broncos, given that he was released just before the regular season and remains unsigned. Lynch did not win the starting job in the 2016 and 2017 training camps and did not offer enough optimism for the team to try him as the full-time starter and let him work through issues. Lynch lost the backup job to Chad Kelly this past summer, though Kelly was released in October after an arrest following a team Halloween party.

The Broncos' 2017 draft class, in particular, had almost no impact, given that five of the eight players drafted are no longer on the current roster, and a sixth player -- tight end Jake Butt -- spent most of his second consecutive season on injured reserve because of knee injuries.

Left tackle Garett Bolles is the only current starter from the class of '17, and he has struggled mightily at times, especially with penalties, as he's tried to learn on the job. Bolles had a league-leading 10 holding penalties in '17 to go with seven holding penalties in the team's first eight games this season.

Elway also traded the team's longest-tenured player in October when wide receiver Demaryius Thomas was shipped to the Texans. After the trade, Thomas publicly questioned the team's trustworthiness and the coaching staff's willingness to listen to players.