The present invention relates to a new series of compounds having general formula (I) and the optical isomer or enantiomer forms thereof, which belong to the family of sulforaphane derivatives. The invention also relates to the production method thereof. The invention further relates to the multiple medical (pharmaceutical, homeopathic and phytotherapeutic), food, cosmetic and dietary uses of said series of compounds, especially the use thereof in the prevention and/or treatment of diseases and any type of illness or damage associated with an oxidative process or which, although not involved in said process, are mediated by the Nrf2 transcription factor, such as, for example, cancer. The compounds can be used alone or, alternatively, encapsulated in cyclodextrins.