The present invention relates to paste-like masses that can be used in electrochemical elements, comprising a heterogeneous mixture of (A) a matrix containing or comprising at least one organic polymer, precursors thereof, or prepolymers thereof, (B) an electrochemically activatable inorganic or largely inorganic liquid that does not dissolve the matrix or essentially does not dissolve the matrix, and, if required, (C) a powdery solid that is essentially inert relative to the electrochemically activatable liquid. The invention furthermore relates to self-supporting layers or layers that are placed on a substrate, comprising a heterogeneous mixture of (A) a matrix containing or comprising at least one organic polymer as defined in any of claims 1 through 7, (B) an electrochemically activatable inorganic or largely inorganic liquid that does not dissolve the matrix or essentially does not dissolve matrix, and if required, (C) a powdery solid that is essentially inert relative to the electrochemically activatable liquid, and composite layers with electrochemical properties that contain such layers. The layers and composite layers can be used advantageously for producing batteries, low-temperature fuel cells, solar cells, or electrochemical sensors.