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40px|left Gymnastics at the 1980 Summer Olympics was represented by 14 events: 6 for women and 8 for men. All the events were held at the Sports Palace of the Central Lenin Stadium (at Luzhniki, south-western part of Moscow) from July 20 to July 25.

Scoring on the vault in the event finals was different from that at the 1976 Summer Olympics: an average of two vaults was taken into account, instead of taking the best of two scores. This rule was adopted by the FIG in 1977 Judging system was basically the same, as at the previous Olympics.

Men's Events
In tables below "C" stands for "Compulsory exercises" and "O" stands for "Optional exercises".

Score computation examples:
 * All-around. In the team competition Roland Bruckner's total "C" value was 58.65 and his total "O" value was 58.25. Hence his "Prelim." value is (58.65+58.25)/2=58.45. His "Final." mark, which is the sum of marks for FX, PH, RG, VT, PB, earned in the all-around, is 58.85. And his total score for the all-around is "Prelim."+"Final."=117.300
 * Horizontal bar (for other apparatus events computation is similar). In the team competition Michael Nikolay's value for HB was 9.75, and his "O" value for HB was 9.60. Hence his "Prelim." value is (9.75+9.60)/2=9.675. On the horizontal bar he then scored 9.85, which is his "Final" value for HB. And his total score for the horizontal bar is "Prelim."+"Final."=19.525

Team competition
Team score for each of the routines is the sum of scores of all team members in that routine, except the lowest of them, which is discarded. Total team score is the sum of team's scores in the routines.

Women's Events
The Soviet women's gymnastics team finished the 1980 Summer Olympics with 8 medals, the same as in Montreal but less than they had won at any previous Olympics. In percentage terms they won 38% of the medals awarded,less than at any previous Olympics. The USSR won only 1 AA medal. In each Olympics before that they had always won 2 and 1960 Summer Olympics had won all 3. At Olomouc 84 and 1988 Summer Olympics they would win 2 again. The Soviet team won the team gold medal by 1.4 points.They had won team gold in Montreal by 3.2 points. In bars event final 5 of the 6 gymnasts won medals (2 Romanians,2 East Germans,1 Soviet). The unlucky gymnast by 0.05 was a Soviet.

Romania won 7 medals,the same number as they had won in Montreal. For the first time ever at the Olympics a Romanian gymnast medals on each piece of apparatus in event finals. This they had never achieved before and achieved only once again in the next 6 Olympics. They won 2 gold,1 silver,2 bronze in event finals - only 1 bronze less than the USSR. Of the 7 perfect scores awarded at the 1980 Summer Olympics 4 went to Romanian gymnasts,2 to Soviet and 1 to an East German. At Montreal in 1976 between the team competition and AA finals Nadia Comaneci was deducted 1.2 points from her start values. In Moscow 1980 she was also deducted 1.2 points. Or to put it another way - for the 11 routines Comaneci was deducted 1.2 in Montreal she was deducted 0.7 in Moscow (omitting her team optional bars score where she fell).

In tables below "C" stands for "Compulsory exercises" and "O" stands for "Optional exercises".

Score computation examples:
 * All-around. In the team competition Yelena Davydova's total "C" value was 39.40 and her total "O" value was 39.60. Hence her "Prelim." value is (39.40+39.60)/2=39.500. Her "Final." mark, which is the sum of marks for VT, UB, BB, FX, earned in the all-round, is 39.65. And her total score for the all-around is "Prelim."+"Final."=79.150
 * Floor exercise (for other apparatus events computation is similar). In the "Team competition" event Nellie Kim's "C" value for FX was 9.90 and "O" value for FX was 9.95. Hence her "Prelim." value is (9.90+9.95)/2=9.925. In the floor exercise she scored 9.95, which is her "Final" value for FX. And her total score for floor exercise is "Prelim."+"Final."=19.845

Team competition
Team score for each of the routines is the sum of scores of all team members in that routine, except the lowest of them, which is discarded. Total team score is the sum of team's scores in the routines.

Floor exercise
Remark:country names are given in the form they were used in the official documents of the IOC in 1980.