Here we demonstrate that both, tunnel magnetoresistance (TMR) and resistive switching (RS), can be observed simultaneously in nanoscale magnetic tunnel junctions. The devices show bipolar RS of 6% and TMR ratios of about 100%. For each magnetic state, multiple resistive states are created depending on the bias history, which provides a method for multibit data storage and logic. The electronic transport measurements are discussed in the framework of a memristive system. Differently prepared MgO barriers are compared to gain insight into the switching mechanism. (C) 2009 American Institute of Physics. [doi: 10.1063/1.3224193]