The way in which a text is written can be a barrier for many people. Automatic text simplification is a natural language processing technology that, when mature, could be used to produce texts that are adapted to the specific needs of particular users. Most research in the area of automatic text simplification has dealt with the English language. In this article, we present results from the Simplext project, which is dedicated to automatic text simplification for Spanish. We present a modular system with dedicated procedures for syntactic and lexical simplification that are grounded on the analysis of a corpus manually simplified for people with special needs. We carried out an automatic evaluation of the system’s output, taking into account the interaction between three different modules dedicated to different simplification aspects. One evaluation is based on readability metrics for Spanish and shows that the system is able to reduce the lexical and syntactic complexity of the texts. We also show, by means of a human evaluation, that sentence meaning is preserved in most cases. Our results, even if our work represents the first automatic text simplification system for Spanish that addresses different linguistic aspects, are comparable to the state of the art in English Automatic Text Simplification.