Recently, some pattern matching algorithms allowing gaps were introduced in Crochemore et al. [Approximate string matching with gaps. Nordic Journal of Computing, 9 (2002):54–65, 2002], where upper-bounded, strict-bounded and unbounded gaps were considered. In this paper we further extend these restrictions on the gaps to permit lower-bounded and (lower-upper)-bounded gaps that we simply refer to as (a,b)-bounded gaps. We give formal definitions for these problems as well as their respective algorithmic solutions.