Don’t use the preposition of after the adjective responsible. Use for:
✗ Parents must be responsible of their children’s behaviour.
✓ Parents must be responsible for their children’s behaviour.
✗ When an animal creates a problem, it is the owner who is responsible of this.
✓ When an animal creates a problem, it is the owner who is responsible for this.
You can also use the pattern responsible for doing something:
He was responsible for ensuring that the organization maintained its independence.