The phrase "a steady procession" is correct and usable in written English.
It can be used to describe a continuous and unchanging flow of people, events, or things moving in a particular direction.
Example: "As the sun set, a steady procession of cars made their way down the winding road."
Alternatives: "an unbroken stream" or "a constant flow".
Secondly, the animals did not march to their deaths in a steady procession over the centuries.
Word of mouth has turned out a steady procession of onlookers.
A steady procession of people, as purposeful as ants, wound its way along undulating paths toward the entrance.
A steady procession takes shape to and from the outhouse, along planks set into the thick Siberian mud.
The Lodge committee, meanwhile, maintained its equanimity, with a steady procession of generals and officials recounting the success and benevolence of American operations.
One allows a steady procession of changes, each announced in turn, discussed, weighed for its merits, perhaps discussed in parliament, eventually accepted and implemented with care and precision.
Trump has had only had good things to say about Ailes ever since ex-Fox host Gretchen Carlson filed a sexual harassment suit against Ailes, which led to a slow and steady procession of women who came forward alleging similar, and sometimes much darker, treatment by Ailes.
Chris Gayle, on 42 from 24 balls, including nine fours, lost his off stump to a yorker from Paul Havell and the steady procession of West Indian batsmen back to the pavilion had begun.
Not far from the finish, the Princeton men watched the steady procession of black tank tops and prepared for their own race.
Only the steady procession of cars driving on the left side of the road indicates that these woods are actually in the center of London.
The film is directed by Valerie Faris and Jonathan Dayton, who made "Little Miss Sunshine" (2006), and, as in that winsome fable, the steady procession of setups and payoffs can feel suspiciously pat.
