NOVELTY - A battery comprises a housing (10) that contains at least two cells (50, 80) connected in series comprising spirally wound electrode assemblies. Each assembly (30) has positive (52) and negative (60) electrode layers separated by a polymer electrolyte.    USE - The battery is for video cameras, cellular phones and portable computers.    ADVANTAGE - The battery has a spiral-wound electrode-type construction that does not require the use of expensive separators. It can generate cell voltages of 3 or more volts while using less-expensive lower voltage components. An easy to manufacture multi-cell construction using conventional electrode winding equipment is made possible. The use of a polymer electrolyte that does not cause inter-cell leakage current eliminates the need for separate sealed containers and prevents physical contact between the positive and negative electrode layers. The elimination of separate sealed containers results into a space-efficient disposal of the electrochemical cells in the battery housing. Since a multi-cell, spiral wound electrode assembly is made possible, higher voltage batteries that use lower voltage cells using less-expensive lower components may be manufactured.    DETAILED DESCRIPTION - An INDEPENDENT CLAIM is also included for a method of assembling a multi-cell battery comprising: (a) forming a first electrochemical cell by winding alternating layers of a positive electrode, a negative electrode and a polymer electrolyte; (b) electrically coupling one of the negative and positive electrodes of the cell to a second electrochemical cell's electrode of opposite polarity; (c) forming the second electrochemical cell by winding alternating layers of a positive electrode, a negative electrode and a polymer electrolyte; and (d) placing the first and second wound cells in a battery housing.    DESCRIPTION OF DRAWING(S) - A cross-sectional diagram of the battery is shown.    Housing (10)    Spiral-wound electrode assembly (30)    Insulating layer (45)    Electrochemical cells (50, 80)    Positive electrode (52)    Negative electrode (60)