Let $${\left\{\mathsf{A}_j|j=0,1,\ldots,rank(g)\right\}}$$ A j | j = 0 , 1 , … , r a n k ( g ) be the fundamental generators of the generalized q-Onsager algebra $${{\cal O}_{q}({\widehat{g}})}$$ O q ( g ^ ) introduced in Baseilhac and Belliard (Lett Math Phys 93:213–228, 2010), where $${\widehat{g}}$$ g ^ is a simply laced affine Lie algebra. New relations between certain monomials of the fundamental generators—indexed by the integer $${r\in\mathbb{Z}^{+}}$$ r ∈ Z + —are conjectured. These relations can be seen as deformed analogs of Lusztig’s rth higher order q-Serre relations associated with $${{\cal U}_q({\widehat g})}$$ U q ( g ^ ) , which are recovered as special cases. The relations are proven for $${r\leq 5}$$ r ≤ 5 . For r generic, several supporting evidences are presented.