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The phrase "are progressing smoothly" is correct and usable in written English.
It can be used to describe a situation or process that is moving forward without any issues or difficulties.
Example: "The project timelines are progressing smoothly, and we expect to meet our deadlines without any delays."
Alternatives: "are advancing well" or "are moving along seamlessly".
Exact(2)
PARIS, Oct. 22 - While patients are panicking over a shortage of flu vaccine in the United States, vaccination programs in Europe are progressing smoothly with a good supply of medicine, health authorities say.
Speaking in St Petersburg, where the qualifying draw for the 2018 World Cup is taking place, the 54-year-old said his successor should be happy because plans for the tournament in Russia are progressing smoothly.
Similar(58)
The integration of Avincis is progressing smoothly and the business is performing as expected.
It added, "All preparatory work for the congress is progressing smoothly".
"The project is progressing smoothly," said Guo Shuyan, deputy director of the State Council Three Gorges committee.
Back at the Golden Nugget, though, the tournament is progressing smoothly, by no means a foregone conclusion.
His project was progressing smoothly when Leiweke proposed to Anschutz, in effect, that they become Roski's competition.
Work was progressing smoothly.On December 30th, Mr Zhu visited the dam site for the first time, and sang a very different song.
Matters had been progressing smoothly enough early in the piece, although the fall of Alastair Cook for his third fifty of the series was cause for concern.
The manual recount was progressing smoothly and swiftly Saturday in most parts of the state, with new votes being recorded for both Vice President Al Gore and Gov. George W. Bush.
The plan seemed to be progressing smoothly, and the deal was ready to go down when Ead learned that the property had been sold to someone else.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com