There are phenomena bounded into positive intervals which show an excessive number of zero values, making it difficult the application of standard modeling procedures. To overcome such a problem, a two-part model is often employed. The model involves two stochastic models: the first governs whether the response variable is zero or positive and the second, conditional on its being positive, models the bounded variable. In this work, we extend this modeling framework to cope with measurement errors affecting the dependent variables. The performance of the proposed approach compared to a naive procedure, which ignores the measurement errors, is evaluated through a Monte Carlo simulation study.