Abstract This paper extends the linear multi-state consecutively-connected system (LMCCS) to the case of LMCCS-MN, where MN denotes the dual constraints of m consecutive gaps and n total gaps. All the nodes are distributed along a line and form a sequence. The distances between the adjacent nodes are usually non-uniform. The nodes except the last one can contain statistically independent multi-state connection elements (MCEs). Each MCE can provide a connection between the node at which it is located and the next nodes along the sequence. The LMCCS-MN fails if it meets either of the two constraints. The universal generating function technique is adopted to evaluate the system reliability. The optimal allocations of LMCCS-MN with two different types of failures are solved by genetic algorithm. Finally, two examples are given for the demonstration of the proposed model.