Groznyy (Fearsome) was the lead ship of the Soviet Navy Project 58 Groznyy-class Guided Missile Cruisers, also known as the Kynda Class. Originally designated a destroyer, the vessel was reclassified as a cruiser on 29 September 1962.

Launched on 26 March 1961, Groznyy was initially accepted into the Northern Fleet. After visits from General Secretary Nikita Khrushchev and Admiral Sergey Gorshkov on 4 May 1962, the ship undertook tests that culminated in the successful launch of two P-35 missiles in front of Khrushchev on 22 July. The ship undertook the first successful deck landing and take-off of the mid-course guidance derivative of the Kamov Ka-25 in 1966 and was transferred to the Black Sea Fleet on 5 October that year.

The ship served globally, including visits to Varna, Bulgaria in August 1967, Tartus, Syria in 1968, Havana, Cuba, in June 1969, Fort-de-France, Martinique in August 1969, Split, Yugoslavia, and Alexandria, Egypt in 1972, Casablanca, Morocco in April 1972, Marseille, France in July 1973, Tobruk, Libya in November 1985, Rostock, East Germany in July 1987 and Szczecin, Poland in July 1988. Groznyy took part in the ''Atlantika-84'' exercise in the Barents and Norwegian Seas in March 1984 and tracked US Navy task forces led by the aircraft carriers USS Coral Sea and USS Saratoga as part of operations in the Mediterranean Sea between 9 August 1985 and 4 February 1986.