Summary: We focus on the problem of approximate matching of strings that have been compressed using run-length encoding. Previous studies have concentrated on the problem of computing the longest common subsequence (LCS) between two strings of length \(m\) and \(n\), compressed to \(m'\) and \(n'\) runs. We extend an existing algorithm for the LCS to the Levenshtein distance achieving \(O(m'n+n'm)\) complexity. Furthermore, we extend this algorithm to a weighted edit distance model, where the weights of the three basic edit operations can be chosen arbitrarily. This approach also gives an algorithm for approximate searching of a pattern of \(m\) letters (\(m\)’ runs) in a text of n letters (\(n'\) runs) in \(O(mm'n')\) time. Then we propose improvements for a greedy algorithm for the LCS, and conjecture that the improved algorithm has \(O(m'n')\) expected case complexity. Experimental results are provided to support the conjecture.