When it was proposed that an English version of my book on stability and oscillation in differential and differential-difference equations be published, my first intention was to modify it substantially. Indeed, although the Rumanian original appeared in 1963, most of it was written in 1961. In the meantime, progress which deserved to be reported was achieved in all the fields covered in the book. Many remarkable works appeared in the United States. However, the desire not to delay the appearance of this book too much finally prompted me to renounce the initial plan and to content myself with making extensive changes only in the last chapter on systems with time lag.