Clause 4.1. says:
"These processes shall be managed by the organization in accordance with the requirements of this International Standard."
I guess by words "these processes" are ment processes that are identified as needed for quality management system (clause 4.1 a))...

Emmm then what are the requirements of ISO 9001 for process management then? Well all stated in Standards clauses: such process should be established, such process should be performed including a and b and c and so on...
But how could sound this 4.1. requirement explained in quality manual?

MD said:

...what are the requirements of ISO 9001 for process management then?...

MD

I hope I understand your question correctly.

As I read the ISO Standard, the requirements for process management are specified in the following clauses:
- 6.3 Infrastructure,
- 6.4 Work environment,
- 7.5.1 Control of production and service provision, and
- 7.5.2 Validation of processes for production and service provisions.

All of Clause 7.0 Product Realization, address various processes needed to provide a product or service.

I hope I have provided some help. If not, keep reading and I'm sure others will provide you with better explanations.

Best Regards,
Hank Fowler
:)