If all directors in company resign

Dear members,

I have a question related to a private limited comapny wholly owned by a foreign shareholder. 

What happens if both directors (Indian) of this company resigns? They were incidentally the promoters as well, but eventually with more investment by the forsign shareholder, the company belongs to him (99.99%)

The directors wish to resign, whose responsibility does it becomes to appoint new directors? What will be the process here? Is there any other way? 

Thanks!