NOVELTY - The method comprises operating a fuel cell to produce a cathode exhaust stream (22) comprising an electrolyte vapor, water vapor and heat, separating the electrolyte vapor and the water vapor from the exhaust stream using a membrane condenser, directing the exhaust stream to contact a first side of a membrane of the condenser, condensing the electrolyte vapor on the first side of the membrane (74), condensing the water vapor inside the membrane, and drawing the condensed water from the membrane to a second side of the membrane. The membrane comprises ceramic material.    USE - The method is useful for recovering water and electrolyte such as phosphoric acid from an exhaust stream of a fuel cell.    ADVANTAGE - The method ensures efficient and economical recovery of water and electrolyte from the exhaust stream of the fuel cell using a corrosion resistant membrane condenser thus preventing contamination of the water with potentially corrosive electrolytes and improving the shelf life and performance of the fuel cell system.    DETAILED DESCRIPTION - The method comprises operating a fuel cell to produce a cathode exhaust stream (22) comprising an electrolyte vapor, water vapor and heat, separating the electrolyte vapor and the water vapor from the exhaust stream using a membrane condenser, directing the exhaust stream to contact a first side of a membrane of the condenser, condensing the electrolyte vapor on the first side of the membrane (74), condensing the water vapor inside the membrane, and drawing the condensed water from the membrane to a second side of the membrane. The membrane comprises ceramic material and multiple porous layers. The condensed electrolyte vapor is collected and then reintroduced into the fuel cell. The condensed water is collected from the second side of the membrane, and joins a cooling fluid in contact with the second side of the membrane. The porous layers comprise pores having a size of 40-100 Angstroms, which is smaller than a molecular size of the electrolyte, but larger than a molecular size of the water. The condenser is operated in fluid communication with the fuel cell to recover heat from the cathode exhaust stream, and comprises a membrane tube (72) having an outer wall (76) and an inner wall (78) with multiple porous layers between the outer wall and inner wall. A cooling tube containing cooling fluid is positioned inside the membrane tube to create a space between the inner wall of the membrane tube and an outer wall of the cooling tube. An INDEPENDENT CLAIM is included for a system for recovering water and electrolyte (88) from an exhaust stream of a fuel cell.    DESCRIPTION OF DRAWING(S) - The figure shows an end view of a membrane tube.    Exhaust stream (22)    Membrane tube (72)    Membrane (74)    Outer wall (76)    Inner wall (78)    Electrolyte. (88)