It is well-known that the logarithmic coefficients play an important role in the development of the theory of univalent functions. If S denotes the class of functions f ðzÞ = z + Σ∞n=2anzn analytic and univalent in the open unit disk U, then the logarithmic coefficients γnðf Þ of the function f ∈ S are defined by log ðf ðzÞ/zÞ = 2Σ∞n=1γnðf Þzn. In the current paper, the bounds for the logarithmic coefficients γn for some well-known classes like Cð1 + αzÞ for α ∈ ð0, 1 and CVhplð1/2Þ were estimated. Further, conjectures for the logarithmic coefficients γn for functions f belonging to these classes are stated. For example, it is forecasted that if the function f ∈ Cð1 + αzÞ, then the logarithmic coefficients of f satisfy the inequalities jγnj ≤ α/ð2nðn + 1ÞÞ, n ∈ℕ: Equality is attained for the function Lα,n, that is, log ðLα,nðzÞ/zÞ = 2Σ∞n=1γnðLα,nÞzn = ðα/nðn + 1ÞÞzn +⋯,z ∈ U:
