Both sides met in the UEFA Cup first round that season
At the dawn of the 1970s, Dutch football dominated Europe at club level and almost internationally in the World Cup.
But by 1976, Ajax's European Cup three in a row was now three years in the past. Meanwhile, the 1976-77 season was the second season back in the top division for Manchester United after their 1974 relegation.
While Ajax and United meet in the Europa League final this Wednesday, they did meet in the early part of the UEFA Cup back in the 1976-77 season, with United prevailing 2-1 on aggregate after a 2-0 home win in the return match.
But who was in that United team for the return game?
Alex Stepney kept goal as he had done for the whole of the previous decade - and would do until 1978 - while Scottish duo Martin Buchan and Stewart Houston would marshal the defence as one of three Scotsmen in the starting lineup.
Houston has gone onto have a long association with Arsenal, serving as a scout for the club, after a brief period as caretaker manager in the mid-90s.
Current Northern Ireland assistant manager Jimmy Nicholl was also part of the United defence on the night.
The midfield featured a then Ireland international in the shape of Gerry Daly who had arrived at Old Trafford from Dublin side Bohemians in 1973 and then remained until 1977 when he would leave for Derby County. All in all, he would make almost 150 appearances for United in his four years there.
Steve Coppell was also part of that midfield, having arrived in 1975 and then remained until 1983 when he had to announce his retirement prematurely as a result of a career ending knee injury.
David McCreery and the late Brian Greenhoff, who had both come through the club's youth ranks, were also in that team as was former Northern Ireland player and manager Sammy McIlroy who was one of three Northern Irishmen in the starting XI against Ajax. He would score one of the goals.
Scotland's Lou Macari was in the midst of his 11 year long Man United career on the night and would also score the other goal against Ajax.
Ex-England international Gordon Hill was the 11th member of that starting team on a night when United were facing Ajax for only the second time in their history, two weeks after the maiden meeting in the first leg.
That 1976 tie was only the second time, United and Ajax have been drawn together in Europe, with the next meeting not coming until the 2011-12 Europa League, the successor to the old UEFA Cup.