A condition of Osserman type, called ϕ-null Osserman condition, is introduced and studied in the context of Lorentz globally framed f -manifolds. An explicit example shows the naturalness of this condition in the setting of Lorentz S-manifolds. We prove that a Lorentz S-manifold with constant ϕ-sectional curvature is ϕ-null Osserman, extending a result stated for Lorentz Sasaki space forms. Then we state a characterization for a particular class of ϕ-null Osserman S-manifolds. Finally, some examples are examined.2000 Mathematics Subject Classification. 53C25, 53C50, 53B30.