NOVELTY - Operation of a fuel cell unit of direct methanol fuel cell (DMFC) type, involves anodic oxidation of alcohol, aldehyde or acid to form carbon dioxide and water; and liberating protons and electrons with use of a catalyst.    USE - For conversion of alcohol, aldehyde or acid to carbon dioxide and water (claimed).    ADVANTAGE - The method achieves higher power density in fuel cells of direct methanol fuel cell (DMFC) type, i.e. higher output power from a fuel cell of a given size and that a fuel cell of given power is less space consuming.    DETAILED DESCRIPTION - Operation of a fuel cell unit of direct methanol fuel cell (DMFC) type, in which an aliphatic, short chain, water soluble, liquid alcohol of formula RCH2OH, aldehyde of formula RCHO or acid of formula RCOOH, is oxidized to carbon dioxide and water, involves either exposing the acid to a anodic reaction for the forming of carbon dioxide, an alcohol with one carbon atom less than the acid, or water (if R is H), and liberating protons and electrons with use of a catalyst (if starting from the acid); exposing the aldehyde to a anodic reaction for the formation of the acid, and liberating protons and electrons with use of a catalyst (if starting from the aldehyde); exposing the alcohol to a anodic reaction for the formation of the aldehyde, and liberating protons and electrons with use of a catalyst (if starting from the alcohol); or (if the formed alcohol with one carbon atom less than the acid is not methanol) exposing the alcohol to a anodic reaction until the formed alcohol is methanol, after which the methanol is exposed to the series of reaction steps.    R=H, CH3, C2H5 or C3H7.    An INDEPENDENT CLAIM is included for a fuel cell unit of DMFC type, where the unit comprises an anodic side having an anode (11) and a catalyst for the anodic reaction, a cathodic side having a cathode (12) and a catalyst for the cathodic reaction, as well as an intermediate membrane (13) that separates the anodic and cathodic sides from each other. The unit is adapted to use as fuel an aliphatic, short chain, water soluble, liquid alcohol (RCH2OH), aldehyde (RCHO) or acid (RCOOH), and in that the unit is divided into several cells that are connected flow-wise in series for the performance of a multi-step anodic reaction. The anodic side and the cathodic side in each cell have a catalyst optimized for the reaction step to be conducted in the cell.    DESCRIPTION OF DRAWING(S) - The figure shows a cross-section view over the fuel cell unit including electrodes, intermediate membranes and flow channels.    cells (1, 2, 3)    anode (11)    cathode (12)    intermediate membrane (13)    surface structure (16)