In the context of efforts to develop at the same time high energy density cathode materials for lithium-ion batteries with low content of critical elements such as cobalt and new cell chemistries for all-solid-state batteries,- a novel family of lithium-rich layered sulfides (Li[LitTi1-t]S2,- 0 ?< ?t ?= ?0.33) belonging to the LiTiS2 – Li2TiS3 system was investigated as intercalation materials. These sulfides,- in which both cations and anions are involved in the redox process,- display common features with isotype Li-rich layered oxides (Li[LixM1-x]O2,- M ?= ?Mn,- Ni,- Co,- …). In a particular composition range,- they exhibit high electrochemical performance with a reversible capacity and an energy density exceeding respectively 265 mAh·g-1 and 600 ?Wh·kg-1,- a very low irreversible capacity in the first cycle,- fast activation and a limited voltage decay. Their operation potential within the electrochemical stability window of sulfide-based fast ionic conductors makes them promising cathode materials for all-solid-state lithium and Li-ion batteries. © 2020 Elsevier B.V.