A method and apparatus for maintaining animal cells in vitro in a substantially arrested state of proliferation with continuous secretion of cell product is disclosed. The cells are retained within a reactor vessel chamber in a semi-rigid matrix having interstices for passage of fluid nutrient medium. Fresh nutrient medium is supplied by perfusion into the matrix through relatively low porosity tubes which are suspended in the reactor chamber and which substantially traverse the matrix; expended medium and cell product is withdrawn through relatively high porosity tubes which also are suspended in the reactor chamber and which substantially traverse the matrix; and oxygenated gaseous medium is supplied by perfusion into the matrix through a selectively-permeable membrane disposed in the reactor chamber.