In a Two Person company, Can a Director become Nominee of the other Director of a the company ?

First of all, there is no concept of "Two person company" under companies act, It's OPC( One person company having only one shareholder and such shareholders need to appoint nominee) ,Now, as per your query, It's Normal Private Limited, In which I'm assuming Father and Son both are shareholder & also director, As per the law, Normal private companies should have min. 2 subscriber/shareholder and 2 director, Now, Father can make nomination of shares By filing SH-13 to company for all or by split certain part of his holding, else after demise succession act applies, Except it, Only body corporates/investors can induct nominee director, If after father demise, Only 1 director remains, then he can call and convene board meeting to appoint additional director to meet min no. of directors, else shareholders can also propose name of director by giving special notice..on valid requisition by calling EGM

Agreed with Chirag, nicely replied, there is no concept of two person Company in the Companies Act, there can be either OPC or Private Limited Company or Public Limited Company and I have tried to solve your doubts as under:

1: There is nothing in the whole Companies Act regarding nominee of Director, there can be either Nominee Director appointed by the Board of Directors or Nominee in shareholding of any member (shareholder) of the Company.

2: As per my opinion, If Son becomes Nominee of Father's Shareholding or Second Joint Shareholder of Father's Shareholding then the shareholding of the Father will be transferred to Son upon demised of the Father, otherwise share transmission procedure needs to be carried out after father's demise and the matter will be decided based upon will and succession.