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Given a graph \( G = (V, E) \) and \( A_1, A_2, \ldots, A_r \), mutually disjoint nonempty subsets of \( V \) where \( |A_i| \leq |V|/r \) for each \( i \), we say that \( G \) is spanning equi-cyclable with respect to \( A_1, A_2, \ldots, A_r \) if there exist mutually disjoint cycles \( C_1, C_2, \ldots, C_r \) that span \( G \) such that \( C_i \) contains \( A_i \) for every \( i \) and \( C_i \) contains either \( \lfloor |V|/r \rfloor \) vertices or \( \lceil |V|/r \rceil \) vertices. Moreover, \( G \) is \( r \)-\(\emph{spanning-equicyclable}\) if \( G \) is spanning equi-cyclable with respect to \( A_1, A_2, \ldots, A_r \) for every such mutually disjoint nonempty subsets of \( V \). We define the spanning equi-cyclability of \( G \) to be \( r \) if \( G \) is \( k \)-spanning-equicyclable for \( k = 1, 2, \ldots, r \) but is not \( (r + 1) \)-spanning-equicyclable. Another approach on the restriction of the \( A_i \)’s is the following. We say that \( G = (V, E) \) is \( r \)-\(\emph{cyclable of order}\) \( t \) if it is cyclable with respect to \( A_1, A_2, \ldots, A_r \) for any \( r \) nonempty mutually disjoint subsets \( A_1, A_2, \ldots, A_r \) of \( V \) such that \( |A_1 \cup A_2 \cup \ldots \cup A_r| \leq t \). The \( r \)-cyclability of \( G \) is \( t \) if \( G \) is \( r \)-cyclable of order \( k \) for \( k = r, r+1, \ldots, t \) but is not \( r \)-cyclable of order \( t + 1 \). On the other hand, the cyclability of \( G \) of order \( t \) is \( r \) if \( G \) is \( k \)-cyclable of order \( t \) for \( k = 1, 2, \ldots, r \) but is not \( (r + 1) \)-cyclable of order \( t \). In this paper, we study sufficient conditions for spanning equi-cyclability and \( r \)-cyclability of order \( t \) as well as other related problems.