NOVELTY - A rechargeable lithium ion battery for use as an energy source for a vehicle includes positive and negative electrodes and non-aqueous electrolyte. The positive electrode comprises a 20-80 micron-thick active material layer (20) of porosity at least 50% formed on a collecting electrode (30). The particle diameter of the positive electrode active material (10) is at most 5 microns.    USE - Energy source for electric and hybrid vehicles.    ADVANTAGE - Improved power density for providing good acceleration is achieved without reducing the high energy density that is important for increasing the driving range. Use of the battery in electric and hybrid vehicles provides reduced environmental pollution.    DETAILED DESCRIPTION - Preferred Features: The thickness of the active material layer (20) is preferably 20-60 microns and the porosity of the active material layer (20) is preferably 50-60%.    The active material layer (20) can comprise a number of such layers having different porosities, where the porosity of the active material layer closer to the collecting electrode is lower.    The active material layer (20) can include a first active material layer of porosity 30-50% formed on the collecting electrode and a second active material layer of porosity 50-60% formed on the first active material layer, where the thickness of each layer is 20-30 microns.    INDEPENDENT CLAIMS are given for:    (a) a rechargeable lithium ion battery that has two positive electrode active material layers, each containing a positive electrode material of different particle diameter and having thickness 20-30 microns; and    (b) vehicles containing a rechargeable lithium ion battery that includes one or two positive electrode active material layers as outlined above.    DESCRIPTION OF DRAWING(S) - The drawing shows a sectional view of an active material layer in a positive electrode according to the invention.    Positive electrode active material (10)    Positive electrode active material layer (20)    Collecting electrode (30)    Separator (40)    Electrolytic solution (50)