A grammar-compressed (GC) string is a string generated by a context-free grammar. This compression model includes LZ78 and LZW compression as a special case. We consider the longest common subsequence problem and the local subsequence recognition problem on a GC-text against a plain pattern. We show that, surprisingly, both problems can be solved in time that is within a polylogarithmic factor of the best existing algorithms for the same problems on a plain text. In a wider context presented elsewhere, we use these results as a stepping stone to efficient approximate matching on a GC-text. © 2011 Springer-Verlag Berlin Heidelberg.