The family of languages generated by Boolean grammars and usable with recursive descent parsing is studied. It is demonstrated that Boolean LL languages over a unary alphabet are regular, while Boolean LL subsets of Σ* a* obey a certain periodicity property, which, in particular, makes the language {aⁿb²ⁿ | n ≥ 0} nonrepresentable. It is also shown that {aⁿbⁿcs | n ≥ 0, s ∈ {a, b}} is not generated by any linear conjunctive LL grammar, while linear Boolean LL grammars cannot generate {aⁿb ⁿc* |n ≥S 0}.