"in an ongoing process" is correct and usable in written English.
You can use it to refer to something that is currently taking place or that is continuously happening. For example, "The company is engaged in an ongoing process of innovation."
"We are in an ongoing process so I cannot anticipate the end, I cannot anticipate the conclusions.
Formative comments, on the other hand, give the student feedback in an ongoing process of learning and skill building.
Finishing one book "just feels like a natural break in an ongoing process; there'll be another along in a year or two's time".
And it sees the fall of Saddam Hussein less as the end of a great diplomatic and military effort than as a step in an ongoing process.
Morgan added that agreement with the council, which was the only remaining substantial creditor, would be the next stage in an ongoing process to save the club.
He did not think of God as strictly unchanging, therefore, but held that God was involved with humans in an ongoing process.
Hairston and Virginia State have been key advocates for eliminating food deserts in Virginia, an ongoing process that has gotten the attention of state legislators.
The "tuning" and the calibration of the HRMA PSF using in-flight data is an ongoing process, as explained in the HRMA calibration pages.
The sequence of the whole genome of CHIKV isolates from mosquitoes in Italy is an ongoing process; when completed, results will be available in GenBank.
The generation of T cells in the thymus is an ongoing process in young animals.
The transformation and improvement of early childhood teacher education in China is an ongoing process.
