"ongoing history" is a correct phrase in written English.
You can use it to describe a history that continues into the present, or something that has a long-running history, for example: "The city has an ongoing history stretching back hundreds of years."
But you cannot push aside an ongoing history of female oppression.
But either way he has now carved his own distinctive niche in the ongoing history of the British sporting summer.
Ongoing history and the extending dispersion of Muslim believers provided the occasion and spur for the compilation of Hadith.
The double motif of "treasured people" and "witness" was not without its tensions as it functioned in ongoing history.
All the while, your mind is reeling, yet again, about the long and ongoing history of white supremacy in this country.
Her ongoing history reflects changes to our political and social environments — a touchstone for our evolving cultural norms, values and ideals.
This thing is enormous and all-pervading, evolving and ongoing, history-altering yet in many respects banal.
Likewise challenging are questions of the priority and efficacy of armed struggle and the terms of engagement in light of recent and ongoing histories of such ventures on the African continent, too many of which involve conscripting children into armies as armed warriors.
Recent insights into rare genetic causes of PD have affirmed the importance of ongoing family history research.
From 2005, he was also the driving force, with Brian Walker, of the ongoing Oxford History of the Irish Book.
And so every day, incrementally, you are adding another layer to a piece of ongoing social history, so it's a work of art in the making.
