1973: three-year-old season

Admetus did not race as a two-year-old and was gelded before making his racecourse debut in 1973, making him ineligible for most European Group One races, which were restricted to entire colts and fillies. After being placed in his first three races, he recorded his first success in the Topcliffe Stakes, a maiden race over ten furlongs at Ripon Racecourse in August, winning "effortlessly" by nine lengths. On his next appearance he contested the valuable William Hill Trophy, a handicap race over one mile at Sandown Park Racecourse and won by three quarters of a length from Old Lucky, to whom he was conceding thirteen pounds. The runner-up went on to win the Royal Hunt Cup in 1974. He was then sent to France and won the Prix de la Porte de Madrid over 2000 metres at Longchamp Racecourse.^[5]

1974: four-year-old season

In 1974, Admetus was transferred to the stable of John Cunnington in France and was ridden in most of his subsequent races by Maurice Philipperon. On his debut for his new trainer, Admetus finished third in the Prix Exbury at Saint-Cloud Racecourse on 21 March and then won a twenty-two runner handicap over 1950 metres at Longchamp. On 11 May the gelding recorded his first Group race win when he carried top weight to victory in Grand Prix d'Evry over 2400 metres, beating the favourite Luenge by two lengths with On My Way in third.^[6]

In the Prix Dollar at Longchamp on 2 June Admetus finished second, beaten three-quarters of a length by Margouillat. Later that month he was sent back to England to contest the Prince of Wales's Stakes (then a Group Two race open to horses of three years and above) over ten furlongs at Royal Ascot. Starting at odds of 6/1 he was restrained by Philipperon at the rear of the field before making rapid progress in the straight. He overtook the odds-on favourite Owen Dudley a furlong from the finish and won comfortably by three-quarters of a length. On 14 July the gelding started 1.7/1 favourite for the Prix Maurice de Nieuil over 2500 metres at Saint-Cloud. He was last of the thirteen runners entering the straight but then produced an impressive burst of acceleration to take the lead in the closing stages and win by three quarters of a lengths from the Preis von Europa winner Acacio d'Aguilar with Ashmore in third. Admetus started favourite for the Prix Gontaut-Biron over 2000 metres at Deauville Racecourse a month later, but failed to reproduce his best form and finished fourth behind the British-trained colt Ksar. Eleven days later he passed the post a neck in front of Ashmore in the Grand Prix de Deauville, but was relegated to second after the racecourse stewards found that Philipperon had struck the runner-up on the head with his whip in the closing stages.^[6]

On his final appearance in Europe in 1974, Admetus finished sixth behind the three-year-old Kamaraan in the Prix du Conseil de Paris over 2400 metres at Longchamp on 20 October. Admetus was then sent to the United States to join Dahlia and Margouillat in a three-strong French challenge for the Washington, D.C.International over one and a half miles at Laurel Park Racecourse. The other overseas challengers were Coup de Feu (Eclipse Stakes) from England, Mistigri (Irish St. Leger) from Ireland and Marduk (Deutsches Derby) from Germany. The three American runners were Big Spruce, Desert Vixen and the Manhattan Handicap winner Golden Don. On 9 November Dahlia, ridden by Lester Piggott, started the odds-on favourite for the International ahead of Big Spruce and Desert Vixen, with Admetus being made a 31/1 outsider. Desert Vixen was sent into the lead by Ron Turcotte, and set a slow pace before accelerating in the back straight, and reached the final turn with a clear advantage over Golden Don, Margouillat and Admetus. The French gelding, however, found a gap on the inside, produced a strong late run to overtake Desert Vixen inside the final furlong and won by three-quarters of a length, with Dahlia finishing well to take third place.^[6] After the race Philipperon said that the winner "showed good spirit and did everything right" whilst Dahlia's rider Lester Piggott said "Admetus is a great horse... we were beaten by real class".^[7]

1975: five-year-old season

On his first appearance as a five-year-old, Admetus looked less than fully fit when sent to England for the John Porter Stakes at Newmbury in April and finished last of the thirteen runners behind Salado. He was off the racecourse for almost five months before returning to run four times in autumn. He won a race over 2200 metres at Longchamp before being sent to North America again and finishing fifth behind Snow Knight in the Canadian International Stakes.^[8]

1976 – 1978: later career

Admetus ran eight times in 1976, winning three minor events, finishing second once and finishing third in the Prix Ridgway at Deauville.^[9] He was then sent back to England to be trained by Fred Winter and was campaigned over hurdles but failed to win in six attempts in 1977 and 1978.^[10]