A tamper sensing system mounted with respect to a protected structure so as to have corresponding stress changes occur therein in response to selected kinds of tamperings with said protected structure, said system characterised by: a first pair of stress affected magnetoresistive memory devices each having a magnetic material layer therein capable of being established in a first one of a pair of alternative magnetization states if in a first kind of stress condition and of being established in a remaining one of said pair of alternate magnetization states if in an alternative second kind of stress condition and with said magnetic material layer in each device of said first pair of stress affected magnetoresistive memory devices having a magnetization in a first direction in one of said pair of alternative magnetization states and in a second direction in that remaining one of said pair of magnetization states, said first pair of stress affected magnetoresistive memory devices being mounted together such that at least one of said first and second directions of a first device of said first pair of stress affected magnetoresistive memory devices parallels at least one of said first and second directions of the remaining device of said first pair of stress affected magnetoresistive memory devices; and a first magnetizing electrical conductor extending adjacent to each device of said first pair of stress affected magnetoresistive memory devices such that providing an electrical current therethrough to generate a corresponding magnetic field thereabout establishes said magnetic material layer of each device of said first pair of stress affected magnetoresistive memory devices in that one of said pair of alternative magnetization states of a first device of said first pair of stress affected magnetoresistive memory devices has said magnetization corresponding thereto to be oppositely directed with respect to said magnetization of the magnetic material layer of the remaining device of said first pair of stress affected magnetoresistive memory devices when each device of said first pair of stress affected magnetoresistive memory devices is provided with the first kind of stress condition. a first pair of stress affected magnetoresistive memory devices each having a magnetic material layer therein capable of being established in a first one of a pair of alternative magnetization states if in a first kind of stress condition and of being established in a remaining one of said pair of alternate magnetization states if in an alternative second kind of stress condition and with said magnetic material layer in each device of said first pair of stress affected magnetoresistive memory devices having a magnetization in a first direction in one of said pair of alternative magnetization states and in a second direction in that remaining one of said pair of magnetization states, said first pair of stress affected magnetoresistive memory devices being mounted together such that at least one of said first and second directions of a first device of said first pair of stress affected magnetoresistive memory devices parallels at least one of said first and second directions of the remaining device of said first pair of stress affected magnetoresistive memory devices; and a first magnetizing electrical conductor extending adjacent to each device of said first pair of stress affected magnetoresistive memory devices such that providing an electrical current therethrough to generate a corresponding magnetic field thereabout establishes said magnetic material layer of each device of said first pair of stress affected magnetoresistive memory devices in that one of said pair of alternative magnetization states of a first device of said first pair of stress affected magnetoresistive memory devices has said magnetization corresponding thereto to be oppositely directed with respect to said magnetization of the magnetic material layer of the remaining device of said first pair of stress affected magnetoresistive memory devices when each device of said first pair of stress affected magnetoresistive memory devices is provided with the first kind of stress condition.