  We study the quantum-mechanical uncertainty relation originating from the
successive measurement of two observables $\hat{A}$ and $\hat{B}$, with
eigenvalues $a_n$ and $b_m$, respectively, performed on the same system. We use
an extension of the von Neumann model of measurement, in which two probes
interact with the same system proper at two successive times, so we can exhibit
how the disturbing effect of the first interaction affects the second
measurement. Detecting the statistical properties of the second {\em probe}
variable $Q_2$ conditioned on the first {\em probe} measurement yielding $Q_1$
we obtain information on the statistical distribution of the {\em system}
variable $b_m$ conditioned on having found the system variable $a_n$ in the
interval $\delta a$ around $a^{(n)}$. The width of this statistical
distribution as function of $\delta a$ constitutes an {\em uncertainty
relation}. We find a general connection of this uncertainty relation with the
commutator of the two observables that have been measured successively. We
illustrate this relation for the successive measurement of position and
momentum in the discrete and in the continuous cases and, within a model, for
the successive measurement of a more general class of observables.
