Varyingly traced to the Blessed Alexander Peresvet of Radonezh (died 1380) and to a certain Vasiliy Ivanovich Peresvet in early-15th-century Dmitrov (NW of Moscow), the family, in the person of Murat Alekseyevich Peresvetov (died 1640) from Rostov Velikij, entered Swedish service in 1613-14 during the Ingrian War.
Immatriculated in 1652 at the Swedish House of Nobility (Riddarhuset), it remained for three centuries a family of officers and lawyers.
All living family members are descendants of lieutenant-colonel Carl-Magnus Pereswetoff-Morath; the surviving line is not represented at the House of Nobility.
Among notable members are Colonel Alexander Pereswetoff-Morath (originally Alexander Moraht Pereswetoff, d. 1687), commandant of Nyenskans (Ingria), and his son, General Carl Pereswetoff-Morath, 1665–1736, active with his two brothers on the Baltic front in the Great Northern War (prisoner of war in Moscow 1704–21).
The 16th-century Muscovite publicist Ivan Semyonovich Peresvetov has been believed to have belonged to another, west Russian, family.