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In the present paper, we establish new inequalities for dual continuous generalized frames by adopting operator methods. The inequalities are parameterized by the parameter <inline-formula> <math display="inline"> <semantics> <mrow> <mi>&#955;</mi> <mo>&#8712;</mo> <mi mathvariant="double-struck">R</mi> </mrow> </semantics> </math> </inline-formula>. These results generalize those obtained by Balan, Casazza and Găvruţa and cover recently obtained results by Zhang and Li in [Zhang, W.; Li, Y.Z. New inequalities and erasures for continuous g-frames. Math. Rep. 2018, 20, 263&#8722;278]. Moreover, we also give an upper bound of inequality for alternate continuous generalized frames in Hilbert spaces. It differs from previous results.