Appointment of Directors:

1. Nomination and Election: Directors can be nominated or elected based on the company's articles of association, shareholders' agreement, or applicable laws. Nomination may occur through internal processes or by external stakeholders, depending on the company's structure.
    
2. Shareholder Approval: In a general meeting of shareholders, the appointment of directors is usually approved through a resolution. Shareholders may also vote on the appointment of directors during the annual general meeting (AGM).
    
3. First Directors: In the case of a newly incorporated company, the first directors may be appointed by the subscribers to the memorandum of association or as per the provisions of the company's articles.
    
4. Appointment by Board: In certain situations, the board of directors may have the power to appoint additional directors, subject to approval by shareholders at the next general meeting.
    
5. Directors' Consent: A person nominated as a director must give their consent in writing to serve as a director. This ensures that individuals are willing and qualified to take on the role.
    
6. Legal Eligibility: Directors must meet the legal eligibility criteria, including age, qualifications, and any disqualifications under company laws.

Removal of Directors:

1. Resignation: Directors can resign from their position by submitting a resignation letter to the board of directors. The resignation takes effect upon receipt or a specified date mentioned in the letter.
    
2. Shareholder Removal: Shareholders can remove a director by passing an ordinary resolution at a general meeting. Special notice is required to propose the removal of a director, and the director has the right to be heard during the meeting.
    
3. Board Removal: In some cases, the articles of association may grant the board the power to remove directors, subject to the provisions of the Companies Act and the company's articles.
    
4. Automatic Removal: Directors may be automatically removed if they become disqualified under the Companies Act or if they fail to meet the criteria specified in the company's articles.
    
5. Court Removal: The court can remove a director based on certain grounds, such as fraud, mismanagement, or persistent default.
    
6. Notice and Opportunity to be Heard: Directors being removed by shareholders or the board must be given proper notice and an opportunity to present their case before the removal is finalized.
    
7. Vacancy Filling: If a director is removed, resigns, or vacates the position, the vacancy can be filled by the appointment of a new director. This can be done by shareholders or the board, as per the company's articles.

It's important to note that the appointment and removal of directors are significant decisions that impact the governance and direction of the company. Companies must adhere to legal requirements, follow the provisions in their articles of association, and ensure transparency and fairness throughout the process.