[en] The 7 s X-ray pulsar 1E 2259+586 and the supernova remnant (SNR) G109.1-1.0 (CTB 109) were observed by BeppoSAX in 1996 November. We confirm the ASCA discovery of an additional low-energy spectral component from 1E 2259+586. This can be modeled as a 0.44 keV blackbody, but we cannot exclude that some, or all, of this emission arises from the part of the SNR that lies within the pulsar's extraction region. The G109.1-1.0 spectrum is well fit with a non-equilibrium ionization plasma model with a best-fit temperature of 0.95 keV. The derived mass for the X-ray emitting plasma (∼15-20 M_[odot]) and its near cosmic abundances imply that the X-ray emission comes mainly from mildly enriched, swept-up circumstellar material. The spectrum is strongly out of equilibrium with an ionization age of only 3000 yr