We studied spectra for 34 accretion-powered X-ray and one millisecond pulsars that were within the field of view of the INTEGRAL observatory over two years (December 2002 - January 2005) of its in-orbit operation and that were detected by its instruments at a statistically significant level (>8 sigma in the energy range 18-60 keV). There are seven recently discovered objects of this class among the pulsars studied: 2RXP J130159.6-635806, IGR/AX J16320-4751, IGR J16358-4726, AX J163904-4642, IGR J16465-4507, SAX/IGR J18027-2017 and AX J1841.0-0535. We analyze the evolution of spectral parameters as a function of the intensity of the sources and compare these with the results of previous studies.