Yes, our blood does contain proteases and nucleases. Proteases are enzymes that break down proteins, and nucleases are enzymes that break down nucleic acids. In the case of blood, proteases and nucleases are involved in a variety of processes such as blood clotting and the degradation of foreign DNA and RNA that may enter the bloodstream. However, the activity of these enzymes is carefully regulated in order to prevent damage to the body's own tissues.