Abstract We consider the longest common subsequence problem in the context of subsequences with gap constraints. In particular, following Day et al. (2022), we consider the setting when the distance (i. e., the gap) between two consecutive symbols of the subsequence has to be between a lower and an upper bound (which may depend on the position of those symbols in the subsequence or on the symbols bordering the gap) as well as the case where the entire subsequence is found in a bounded range (defined by a single upper bound), considered by Kosche et al. (2022). In all these cases, we present efficient algorithms for determining the length of the longest common constrained subsequence between two given strings, and discuss lower bounds for the respective problems.