%!TEX program = xelatex
documentclass{article}

usepackage{fontspec}
newfontfamilyavr{Avenir Next Regular}[Ligatures=TeX]
newfontfamilyavd{Avenir Next Demi Bold}[Ligatures=TeX]
newfontfamilyavdi{Avenir Next Demi Bold Italic}[Ligatures=TeX]
begin{document}
section{}
{avd This is "Avenir Next Demi Bold" font.}
section{}
{avdi This is "Avenir Next Demi Bold Italic" font.}
section{}
textit{avd{This is textit{"Avenir Next Demi Bold" font.}}}
section{}
avr Why the last two have different ``boldness''?
end{document}