  We present detailed JHK surface photometry with ellipse fits of 13 galaxies
selected from previous optical observations as likely candidates for having a
secondary bar or a triaxial bulge within the primary bar. We have found 7
double-barred galaxies, 3 double-barred galaxies with an additional
intermediate structure with twisted isophotes, and 3 galaxies with a bar and
central twisted isophotes. A global analysis of the structural parameter
characteristics in the I- and K-bands is presented. Various numerical models of
galaxies with bars within bars are also analysed using the ellipse fitting
technique and compared to the observations. A thorough review of the possible
hypotheses able to explain this phenomenon is given with emphasis on the most
likely ones.
