The invention relates to the use of a composition comprising adult human liver-derived progenitor cells, such as heterologous human adult liver-derived progenitor cells (HHALPC), for the treatment of a patient having nonalcoholic fatty liver disease (NAFLD), such as non-alcoholic fatty liver (NAFL)or non-alcoholic steatohepatitis (NASH), or wherein the patient is at risk of developing NASH. The treatment comprises a step of administering to said patient an amount of said composition which comprises a dose of 0.25 to 2.5 million said progenitor cells per kg body weight; wherein the composition is substantially free of an effective amount of an anticoagulant, and wherein the patient does not receive any co-treatment with an anticoagulant