A non-volatile random access memory (NVRAM) of the type with magnetoresistive memory elements (1) connected by sets of non-intersecting conductor sense lines (3, 4) which define the address of each memory element (1) and are connectable to a magnetic write/read recording unit. The memory elements are a plurality of magnetoresistive submicron dots or wires (1) embedded in a membrane (2) through which the submicron dots or wires extend. The sets of non-intersecting conductor sense lines (3, 4) are connected to the opposite ends of the submicron dots or wires (1) on opposite sides of the membrane. Each magnetoresistive submicron dot or wire (1) is composed of ferromagnetic material or a combination of ferromagnetic and non-ferromagnetic materials having at least two magnetic states ("0"; "1"), writeable by passing at an appropriate external field a writing current pulse (iw) in its conductor lines (3, 4, 5) sufficient to switch its magnetic states and readable by passing a an AC or DC current (ir) in its conductor lines below the level for switching its magnetic states.