A sequence of points in a topological group is slowly oscillating if for any given neighborhood of , there exist and such that if and . It is well known that in a first countable Hausdorff topological space, a function is continuous if and only if is convergent whenever is. Applying this idea to slowly oscillating sequences one gets slowly oscillating continuity, i.e. a function defined on a subset of a topological group is slowly oscillating continuous if is slowly oscillating whenever is slowly oscillating. We study the concept of slowly oscillating continuity and investigate relations with statistical continuity, lacunary statistical continuity, and some other kinds of continuities in metrizable topological groups.