NOVELTY - A flexible, asymmetric electrochemical cell comprises: (A) a sheet of graphene paper as first electrode having nano graphene platelets having a platelet thickness of less than 1 nm, where the first electrode has electrolyte-accessible pores; (B) a thin-film first separator and electrolyte; and (C) a thin-film or paper-like second electrode which is different in composition than the first electrode; and where the separator is sandwiched between the first and second electrode to form a flexible laminate configuration.    USE - As a flexible, asymmetric electrochemical cell used as a supercapacitor or electric double layer capacitor; and in a battery (claimed).    ADVANTAGE - The asymmetric supercapacitor cells with different nano graphene platelet (NGP)-based electrodes exhibit an exceptionally high capacitance, specific energy, and stable and long cycle life. The cell increases the effective interface area without compromising the tolerable voltage through the creation of large amounts of inter-graphene in an NGP-based electrode; reduce the electrode resistance by forming a network of interconnected NGPs to maintain a network of electron-conducting paths; and provides a composite electrode that exhibit a high pseudo-capacitance through the presence of selective active nano-particles, such as transition metal oxides, carbides, or nitrides, or conductive polymer-graphene redox pairs, or through surface functionalization of the invented graphene electrode.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are included for following:    (1) a flexible electrochemical capacitor or supercapacitor, comprising: a first paper-like electrode comprising nano graphene platelets and several pores accessible by an electrolyte, where the first electrode has a specific surface area of greater than 100 m2/g; a second paper-like electrode comprising nano graphene platelets and several pores accessible by the electrolyte, where the second electrode has a specific surface area of greater than 100 m2/g; and a paper-like or porous electrode separator disposed between the first and second electrodes, where the separator comprises the electrolyte;    (2) a flexible hybrid electrochemical cell comprising a first electrochemical which is used as a supercapacitor; and a second energy storage or conversion cell in a working relation to the first electrochemical cell, where the energy storage or conversion cell is selected from battery, fuel cell, and/or photovoltaic or solar cell; and    (3) an asymmetric electrochemical cell comprising: a first electrode comprising nano graphene platelets having a platelet thickness of less than 1 nm, where the first electrode has electrolyte-accessible pores, a first separator and electrolyte, and a second electrode which is different in composition than the first electrode, and where the separator is sandwiched between the first and second electrode; and further comprising: (D) a second separator containing electrolyte, where the second separator is in physical contact with the second electrode, and (E) a third thin-film or paper-like electrode in contact with the second separator.    DESCRIPTION OF DRAWING(S) - The figure shows examples of flexible, asymmetric electrochemical cells.