In this note, a method of constructing conditional exponential bases in some. Banach spaces of analytic functions is presented. The method of constructing basic families due to Figà-Talamanca is generalized. Concrete applications and examples of conditional basic families in the space of multipliers of power series with the sequence of Taylor coefficients from l^p, in the space of multipliers of Cauchy-type integrals, and in other spaces are given.