1978: three-year-old season

Inkerman began his racing career in a maiden race over ten furlongs at the Curragh on 13 May and won by four lengths from his stablemate Noble Quillo. Two weeks later he was stepped up in class for the Gallinule Stakes over one and a half miles and won again, coming home six lengths clear of Encyclopedia. The colt quickly became regarded as a major contender for The Derby ten days later especially after Lester Piggott opted to ride the colt. Piggott was looking to follow up his victories on Empery 1976 and The Minstrel in 1977 and win the race for a record ninth time. Despite his lack of experience Inkerman started favourite but after racing close to the lead in the early stages he dropped away quickly in the straight and finished twenty-first of the twenty-five runners behind Shirley Heights. It was reported that the colt had "swallowed his tongue".^[2]

Inkerman was equipped with a tongue strap when he ran in the Irish Derby at the Curragh on 1 July. He produced a much better performance than he had done at Epsom and finished fourth behind Shirley Heights, Exdirectory and Hawaiian Sound, beaten by less than a length and a half by the winner. The colt's next two runs were disappointing. At the end he finished fourth to Sexton Blake in the Gordon Stakes at Goodwood Racecourse after Piggott employed exaggerated waiting tactics. In the Blandford Stakes at the Curragh in August he came home third behind Valley Forge and Rathdowney, looking to be unsuited by the prevailing soft ground.^[2]

On 23 September the third running of the Joe McGrath Memorial Stakes over ten furlongs at Leopardstown Racecourse on 23 September saw Inkerman, with Piggott in the saddle, start the 13/8 favourite in a seven-runner field. Seton Blake started second favourite ahead of the filly More So while the best of the other runners appeared to be the four-year-old Orchestra (winner of the John Porter Stakes). Inkerman went to the front soon after the start and never looked to be in the slightest danger of defeat as he turned into the straight with a clear advantage and won by four lengths from Sexton Blake.^[2]

In October Inkerman was put up for auction at Hollywood Park and was sold for $1,000,000, a world record auction price for a horse in training.^[2] He remained in the United States and ran thenceforth in the colours of Edward Hudson.

For his efforts in 1978, Inkerman was given a rating of 126 by the Independent Timeform organisation, making him even pounds inferior to their top-rated three-year-old Ile de Bourbon. In the official International Classification he was rated six pounds behind Ile de Bourbon, making him the seventh-best three-year-old colt of the season in Europe.^[2]

1979: four-year-old season

In 1979 Inkerman was based in California where he was trained by Charlie Whittingham. The colt took time to acclimatise to North American racing and was beaten in his first three starts before winning an allowance race at Hollywood Park on 17 June. In July he was stepped up in class and showed improved form to finish third in both the American Handicap and the Sunset Handicap.^[5]

1980: five-year-old season

In 1980 Inkerman continued to race exclusively in California. He was beaten in allowance races on his first two starts and than ran second to Bold Tropic in the American Handicap. On 21 July on his final racecourse appearance, he made his second attempt to win the Sunset Handicap. Ridden by Willie Shoemaker, he won the race, beating his front-running stablemate Obraztsovy into second place.^[6][5]