She entered politics in 1983 with Ucedé, and later became an influential member of the Menem administration, leading the successful privatisation of the ENTel phone company and as secretary of Natural Resources.
Alsogaray's great-grandfather had a role as Admiral Guillermo Brown's adjutant in the 1845 Battle of Vuelta de Obligado, which established Argentine control over the lower Paraná River, and both his father and grandfather had been colonels in the Argentine Army.