NOVELTY - A composite body, comprising a hot laminated stack of specified separator, cathode and anode layers, is new.    USE - The composite body is used for production of an electrochemical cell, in a sensor, an electrochromic window, a display, a capacitor or an ion conductive foil and the cell is used in automobile batteries, appliance batteries, flat batteries, on-board batteries, batteries for static applications, electrotraction batteries or polymer batteries (claimed), the battery being especially a lithium ion battery.    ADVANTAGE - The composite bodies are mechanically stable and can be used directly as an electrochemical cell.    DETAILED DESCRIPTION - A novel composite body comprises (A) one or more separator layers (Aa) which is free from electronically conductive electrochemically active compounds and which consists of a combination (Ia) containing 1-100 wt.% of a mixture (IIa) and consisting of (by wt.) 1-95% preferably basic solids (III) of 5 nm to 20 mu primary particle size and 5-99% polymeric material (IV) obtained by polymerizing (a) 5-100 wt.% condensation product (V) of a compound (VI), capable of reacting with carboxylic and/or sulfonic acids or their derivatives, and a molar equivalent quantity of carboxylic and/or sulfonic acid (derivative) having one or more functional groups capable of radical polymerization and (b) 0-95 wt.% further compound (VIII) of number average molecular weight at least 5000 with main or side chain polyether segments; (B) a cathode layer (B) containing an electronically conductive electrochemically active compound capable of releasing lithium ions during charging; and (C) an anode layer (C) containing an electronically conductive electrochemically active compound capable of accepting lithium ions during charging. INDEPENDENT CLAIMS are also included for the following: (i) a similar composite body in which the polymer component (b) is obtained by polymerizing (b1) 5-75 wt.% of a compound (VI) which is different from carboxylic and/or sulfonic acids or their derivatives and which is capable of radical polymerization and (b2) 25-95 wt.% of a further compound (VIII) of number average molecular weight at least 5000 with main or side chain polyether segments; (ii) a process for producing the above composite bodies in which the separator layer(s) (Aa, Ab), the cathode layer (B), the anode layer (C) and optionally an adhesion promoting layer (D) are joined together by hot lamination; and (iii) an electrochemical cell comprising one or more of the above composite bodies.