In this article, the linguistic phenomena of homonymy and polysemy are analyzed as understood by various linguists and lexicographers, such as Lyons (1977), Haensch et al (1982), Cabré (1993) or Vivanco (2003), among others. In addition, this text includes a lexical-semantic analysis of verbal Anglicisms in Spanish which are homonymous and polysemical. It distinguishes between necessary homonym verbs, such as chatear, and unnecessary homonym verbs, for example, aplicar. With regards to the polysemy verbs, there are verbs that inherit polysemy from English (surfear) and those verbs whose polysemy takes place once the borrowed word is established in Spanish (drenar).