An infinite dimensional analytic Lie group is a group which is at the same time an analytic manifold modelled on some locally convex topological vector space such that the group operations are analytic. In order to construct new classes of analytic Lie groups it is useful to have tools at hand ensuring analyticity of nonlinear mappings between locally convex spaces. This talk provides a sufficient criterion for complex analyticity in the case where the modelling space is an (LB)-space, i.e. a locally convex direct limit of an ascending sequence of Banach spaces. These new Lie groups turn out to be regular Lie groups (in Milnor's sense) if the (LB)-space is compactly regular.