NOVELTY - A microfibrous fuel cell element comprises: a microfibrous hollow membrane separator; inner current collector; inner electrocatalyst layer; outer current collector; and outer electrocatalyst layer. At least one of the inner and outer electrocatalyst layers comprises a fiber network (having multiple continuous conductive fibers extending in directions parallel to the longitudinal axis of the element) impregnated with electrocatalyst material.    USE - In fuel cell assembly; for attaching a catalyst structure to a substrate (claimed); in power generation.    ADVANTAGE - The microfibrous fuel cell element develops high quality power sources for use in hand-held or mobile electrical devices, electrically powered vehicles, in distributed power generation applications, based on such microfibrous fuel cells. The microfibrous fuel cell element provide an improved microfibrous fuel cell element with electrocatalytical structures having high mechanical strength and robustness that provide good adhesion to the membrane separator even in consideration of the dimensional changes of such membrane separator during operation; can be manufactured by continuous extrusion on an automated production line, which enables commercial production of such microfibrous fuel cells, enhancing cell uniformity and consistency, and reducing the associated manufacturing costs. The electrocatalyst structure is free of fibers that are not parallelly oriented in relation to the longitudinal axis of such fuel cell.    DETAILED DESCRIPTION - A microfibrous fuel cell element comprises: a microfibrous hollow membrane separator defining a bore side and a shell side; an inner current collector at its bore side; an inner electrocatalyst layer in contact with an inner surface of the membrane separator; an outer current collector at its shell side; and an outer electrocatalyst layer in contact with an outer surface of the membrane separator. The microfibrous fuel cell element has a longitudinal axis. At least one of the inner and outer electrocatalyst layers comprises a fiber network impregnated with an electrocatalyst material. The fiber network comprises multiple continuous conductive fibers extending in directions that are parallel to the longitudinal axis of such microfibrous fuel cell element. The inner fluid passage is provided between the inner electrocatalyst layer and the inner current collector for flow of either a fuel-containing or oxidant-containing fluid. INDEPENDENT CLAIMS are included for the following:    (1) a fuel cell assembly comprises the multiple microfibrous fuel cell elements connected in series and/or parallel and disposed in a housing;    (2) formation (M1) of the microfibrous fuel cell element;    (3) a catalyst structure comprises a fiber network impregnated with an electrocatalyst material. The fiber network comprises multiple conductive fibers that are parallel to one another;    (4) formation (M2) of the catalyst structure involving: forming a fiber network containing multiple conductive fibers that are parallel to one another; and impregnating the fiber network with an electrocatalyst material;    (5) a method (M3) for attaching the catalyst structure to a substrate involving applying an adhesion composition to a surface of the substrate; and attaching the catalyst structure to the surface of the substrate; and    (6) a system for forming a microfibrous fuel cell in a continuous manner.