In species where males provide neither direct benefits nor paternal care, it is typically assumed that female preferences are maintained by indirect selection reflecting genetic benefits to offspring of preferred males. However, it remains unclear whether populations harbour sufficient genetic variation in fitness to support costly female preferences – a problem called the ‘lek paradox’. Here, we ask whether indirect selection on female preferences can be maintained by nongenetic inheritance. We construct a general model that can be used to represent either genetic or nongenetic inheritance, depending on the choice of parameter values. Interestingly, we find that costly preference is most likely to evolve and persist when fitness depends on an environmentally induced factor that can be transmitted over a single generation only, such as an environment-dependent paternal effect. Costly preference can also be supported when fitness depends on a highly mutable factor that can persist over multiple generations, such as an epigenetic mark, but the necessary conditions are more restrictive. Our findings show that nongenetic inheritance provides a plausible hypothesis for the maintenance of costly female preferences in species where males provide no direct benefits to females. Nongenetic paternal inheritance of fitness can occur in species lacking conventional forms of paternal care. Indeed, transmission of paternal condition via sperm-borne nongenetic factors may be more likely to evolve than conventional forms of paternal investment because sperm-borne effects are protected from cuckoldry. Our results furnish a novel example of an interaction between genetic and nongenetic inheritance that can lead to otherwise unexpected evolutionary outcomes.