The synthesis, structures and magnetic properties of two fluorine-intercalated layered manganates, LaSrMnO4F and La1.2Sr1.8Mn2O7F, are reported. Rietveld structure refinement based on time of flight neutron powder diffraction data indicates that both compounds are tetragonal (space group P4/nmm) with cell parameters a=3.77696(7) Angstrom, c=14.1026(8) Angstrom (LaSrMnO4F) and a=3.8103(1) Angstrom, c=21.7220(2) Angstrom (La1.2Sr1.8Mn2O7F). Fluorine occupies interstitial sites in only one of the two rock salt layers available in the unit cell, leading to novel staged intercalation structures. The interstitial fluorine increases the spacing between the two adjacent rock salt layers and thereby causes a significant reduction in the Mn-O apical bonds directed towards the intercalated regions. The Mn valences of both compounds are close to 4, and no long range magnetic order was observed in the title compounds down to 5 K.