The Galactic Center black hole candidate (BHC) GRS 1758-258 has been observed extensively within INTEGRALs Galactic Center Deep Exposure (GCDE) program in 2003 and 2004, while also being monitored with RXTE. We present quasi-simultaneous PCA, ISGRI, and SPI spectra from four GCDE observation epochs, as well as the evolution of energy-resolved PCA and ISGRI light curves on time scales of days to months. We find that during the first epoch GRS 1758-258 displayed another of its peculiar dim soft states like the one observed in 2001, increasing the number of observed occurrences of this state to three. During the other epochs the source was in the hard state. The hard X-ray emission component in the epoch-summed spectra can be well described either by phenomenological models, namely a cutoff power law in the hard state and a pure power law in the dim soft state, or by thermal Comptonization models. A soft thermal component is clearly present in the dim soft state and might also contribute to the softer hard state spectra. We argue that in the recently emerging picture of the hardness-intensity evolution of black hole transient outbursts in which hard and soft states are observed to occur in a large overlapping range of luminosities (hysteresis), the dim soft state is not peculiar. As noted before for the 2001 dim soft state, these episodes seem to be triggered by a sudden decrease (within days) of the hard emission, with the soft spectral component decaying on a longer time scale (weeks). We discuss this behavior in terms of the existence of two independent accretion flows, the model previously suggested for the 2001 episode. (Abridged)
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