The anti-terror agency had summoned Naseem, a professor, and Nayeem, a surgeon, for questioning after it arrested half a dozen separatists including Geelani's son-in-law Altaf Ahmad Shah. They were accused of receiving funds from Pakistan to fuel protests in the Kashmir Valley.
In this case, the NIA had accused separatist and secessionist leaders of working in tandem with terrorist groups including Hafiz Saeed, leader of the Pakistan-based Jamaat-ud-Dawa and banned terrorist outfit Lashkar-e-Taiba.
Geelani's elder son Naeem, who lived in Pakistan for nearly a decade, had returned to Kashmir in 2010 and is seen as the successor to the Geelani-led Tehrek-e-Hurriyat, a separatist conglomerate comprising pro-Pakistan hardline groups.
NIA officials say Geelani's two sons play a key role in the affairs of the Hurriyat faction and are suspected to be closely involved in the process of raising funds from Pakistan received through hawala and their disbursal.
The Geelani brothers had earlier evaded responding to summons from the NIA. Naeem was admitted in a Srinagar hospital following chest pain. Naseem, on the other hand, wanted the agency to summon him through his employer, an agricultural university in the Valley, to enable him to avail travel and dearness allowance.
NIA investigators have questioned several Hurriyat leaders, their relatives and some identified stone throwers in Srinagar after the arrest of seven key Kashmiri separatists -- Nayeem Khan, Altaf Ahmad Shah, Aftab Hilali Shah alias Shahid-ul-Islam, Ayaz Akbar Khandey, Peer Saifullah, Raja Mehrajuddin Kalwal and Farooq Ahmad Dar alias Bitta Karate.
Get Breaking news, live coverage, and Latest News from India and around the world on NDTV.com. Catch all the Live TV action on NDTV 24x7 and NDTV India. Like us on Facebook or follow us on Twitter and Instagram for latest news and live news updates.