For some kind of “higher monodromy”, see Toen: Vers une interpretation galoisienne etc. File Toen web publ gal.pdf.
http://ncatlab.org/nlab/show/monodromy
http://rigtriv.wordpress.com/2010/02/25/monodromy-representations/
http://rigtriv.wordpress.com/2010/03/02/monodromy-and-moduli/
nLab page on Monodromy