  We explore Lie superalgebra deformations of the Killing superalgebras of some
ten-dimensional supergravity backgrounds. We prove the rigidity of the Poincare
superalgebras in types I, IIA and IIB, as well as of the Killing superalgebra
of the Freund-Rubin vacuum of type IIB supergravity. We also prove rigidity of
the Killing superalgebras of the NS5, D0, D3, D4 and D5 branes, whereas we
exhibit the possible deformations of the D1, D2, D6 and D7 brane Killing
superalgebras, as well as of that of the type II fundamental string solutions.
We relate the superalgebra deformations of the D2 and D6 branes to those of the
(delocalised) M2 brane and the Kaluza-Klein monopole, respectively. The good
behaviour under Kaluza-Klein reduction suggests that the deformed superalgebras
ought to have a geometric interpretation.
