The gamma-ray energy spectra of bright blazars of the LAT Bright AGN Sample LBAS) are investigated using Fermi-LAT data. Spectral properties hardness, curvature, and variability) established using a data set accumulated over 6 months of operation are presented and discussed for different blazar classes and subclasses: flat spectrum radio quasars (FSRQs), low-synchrotron peaked BLLacs (LSP-BLLacs), intermediate-synchrotron peaked BLLacs (ISP-BLLacs), and high-synchrotron peaked BLLacs (HSP-BLLacs). The distribution of photon index G, obtained from a power-law fit above 100 MeV) is found to correlate strongly with blazar subclass. The change in spectral index from that averaged over the 6 months observing period is < 0.2-0.3 when the flux varies by about an order of magnitude, with a tendency toward harder spectra when the flux is brighter for FSRQs and LSP-BLLacs. A strong departure from a single power-law spectrum appears to be a common feature for FSRQs. This feature is also present for some high-luminosity LSP-BLLacs, and a small number of ISP-BLLacs. It is absent in all LBAS HSP-BLLacs. For 3C 454.3 and AO 0235+164, the two brightest FSRQ source and LSP-BLLac source, respectively, a broken power law (BPL) gives the most acceptable of power law, BPL, and curved forms. The consequences of these findings are discussed.