This North African species was described in 1870 based on fossil remains that were dated to the Upper Pleistocene, however, some remains apparently turned out to be much younger, thus the species might have survived until about 3000 years BP..
I was unfortunately unable to find any source for that assumption.
The Bluebuck was described in 1766; during the Late Pleistocene, the species was very widespread in South Africa, but the populations began to shrink following climatical changes at the beginning of the Holocene, in historical times, the species was finally restricted to a relict population that inhabited a rather small region at the southern tip of South Africa.
The species had a generally bluish gray fur, the upper lip and a patch in front of the eye were somewhat lighter, the forehead was brown, the belly was whitish.
The Bluebuck was hunted to extinction by European settlers, it is actually the first African mammal to become extinct in historical times, the last individuals were killed in 1799 or 1800.
Depiction from: ‘Francis Harper: Extinct and Vanishing Mammals of the Old World. New York, American Committee for international wildlife protection. Special Publication No. 12. 1945’
North African Hartebeest (Alcelaphus buselaphus ssp. buselaphus)
The North African Hartebeest [which is a monotypic species in my opinion] was once widely distributed all over northern Africa, including Egypt, Algeria, Jordan, Libya, and Morocco, and occurred probably also in Palestine and some parts of Saudi Arabia.
The animal reached a shoulder height of up to 1,5 m.
The North African Hartebeest was already well known to the ancient Egyptians and the Romans and can be found depicted Roman mosaics.
The species begun to disappear during the second half of the 19th century – due to direct hunting, especially during the French conquest of Algeria between 1830 and 1847, when thousands of the antelopes were killed by French soldiers just for amusement.
The last known individual was shot in the year 1925 in Morocco.
Yet, the species may have survived in the wild for a longer time than previously known – some bones, found 1998 in the Dakhla Oasis in Egypt inside of an abandoned hyena burrow could be dated to about 1960.
 A. J. Mills: Report presented to the Supreme Council of Antiquities, Egypt, on the 2000 Season of the Dakhleh Oasis Projekt. Dakhleh Oasis Project SCA Report: 1999/2000 Season
The Kenyan Oribi is one of the about nine subspecies of the Oribi (Ourebia ourebi Zimmerman), a small antelope species that is distributed over several parts of central-, eastern- and even southern Africa; it was apparently restcicted to the slopes of Mt. Kenya.
This form apparently died out in the wild sometimes during the 1960s and was subsequently kept in captivity for some time; its actual extinction date obviously is not known but is believed to be sometimes during the 1980s.
Oribi (Ourebia ourebi), nominate form?
Depiction from: ‘P. L. Sclater; O. Thomas: The Book of Antelopes. London: R. H. Porter 1894-1900’
The Saudi Gazelle, described in 1935, was native to the Arabian Peninsula, where it inhabited sandy acacia plains.
The species disappeared du to excessive hunting and was declared extinct in the wild in 1980 when it very probably was already globally extinct, because all captive individuals were subsequently shown to represent hybrids or different species.
Queen of Sheba’s Gazelle aka. Yemen Gazelle was for some time believed to be a subspecies of the Arabian Gazelle (Gazella arabica (Lichtenstein)) (see photo below) but is now considered a distinct species.
The species inhabited the mountains near city of Ta’izz in southwestern Yemen where it was last seen in 1951 when it apparently still was quite common.
In 1985, a photograph of gazelles taken in a private collection, the Al Wabra Wildlife Farm in Qatar, might show this species, however, this has apparently never been confirmed, nor seems the subsequent fate of these animals to be known.
Queen of Sheba’s Gazelle is now considered extinct with the cause of its extinction being uncertain, however, it most likely was hunted to extinction.