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Let $\{A_j|j=0,1,...,rank(g)\}$ be the fundamental generators of thegeneralized $q-$Onsager algebra $\cal O_{q}(\widehat{g})$ introduced in\cite{BB1}, where $\widehat{g}$ is a simply-laced affine Lie algebra. Newrelations between certain monomials of the fundamental generators - indexed bythe integer $r\in\mathbb{Z}^{+}$ - are conjectured. These relations can be seenas deformed analogues of Lusztig's $r-$th higher order $q-$Serre relationsassociated with ${\cal U}_q({\widehat g})$, which are recovered as specialcases. The relations are proven for $r\leq 5$. For $r$ generic, severalsupporting evidences are presented.

Higher order relations for ADE-type generalized q-Onsager algebras