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For a flag homology sphere $\\Delta$, we show that its $\\gamma$-vector $\\gamma^\\Delta=(1,\\gamma_1,\\gamma_2,\\ldots)$ satisfies: \\begin{align*}\n  \\gamma_j=0,\\text{ for all } j>\\gamma_1, \\quad \\gamma_2\\leq\\binom{\\gamma_1}{2}, \\quad \\gamma_{\\gamma_1}\\in\\{0,1\\}, \\quad \\text{ and }\\gamma_{\\gamma_1-1}\\in\\{0,1,2,\\gamma_1\\}, \\end{align*} supporting a conjecture of Nevo and Petersen. Further we characterize the possible structures for $\\Delta$ in extremal cases. 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For a flag homology sphere $\\Delta$, we show that its $\\gamma$-vector $\\gamma^\\Delta=(1,\\gamma_1,\\gamma_2,\\ldots)$ satisfies: \\begin{align*}\n  \\gamma_j=0,\\text{ for all } j>\\gamma_1, \\quad \\gamma_2\\leq\\binom{\\gamma_1}{2}, \\quad \\gamma_{\\gamma_1}\\in\\{0,1\\}, \\quad \\text{ and }\\gamma_{\\gamma_1-1}\\in\\{0,1,2,\\gamma_1\\}, \\end{align*} supporting a conjecture of Nevo and Petersen. Further we characterize the possible structures for $\\Delta$ in extremal cases. 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