  The cluster of galaxies A2256 was observed by the PCA and HEXTE experiments
aboard the RXTE satellite during the period July 2001 - January 2002, for a
total of 343 ks and 88 ks, respectively. Most of the emission is thermal, but
the data analysis yields evidence for two components in the spectrum. Based on
statistical likelihood alone, the secondary component can be either thermal or
power-law. Inclusion in the analysis of data from ASCA measurements leads to a
more definite need for a second component.Joint analysis of the combined
RXTE-ASCA data sets yields $kT_1 = 7.9^{+0.5}_{-0.2}$ and $kT_2 =
1.5^{+1.0}_{-0.4}$, when the second component is also thermal, and $kT =
7.7^{+0.3}_{-0.4}$ and $\alpha = 2.2^{+0.9}_{-0.3}$, if the second component is
fit by a power-law with (photon) index $\alpha$; all errors are at 90%
confidence. Given the observed extended regions of radio emission in A2256, it
is reasonable to interpret the deduced power-law secondary emission as due to
Compton scattering of the radio producing relativistic electrons by the cosmic
microwave background radiation. If so, then the {\it effective, mean
volume-averaged} value of the magnetic field in the central 1$^{o}$ region of
the cluster -- which contains both the `halo' and `relic' radio sources -- is
$B \sim 0.2^{+1.0}_{-0.1}$ $\mu G$.
