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We present spectra of the 3.3 mum and 11.2 mum polycyclic aromatic hydrocarbon (PAH) features of a large number of stellar sources, planetary nebulae, reflection nebulae, H II regions, and galaxies, obtained with Infrared Space Observatory Short Wavelength Spectrometer. Clear variations are present in the profiles of these features. Most of the sources show a symmetric 3.3 mum feature peaking at similar to3.290 mum, while only very few show an asymmetric 3.3 mum feature peaking at a slightly longer wavelength. The profiles of the 11.2 mum feature are distinctly asymmetric. The majority of the sources has a 11.2 mum feature peaking between 11.20 and 11.24 mum, with a very steep blue rise and a low tail-to-top ratio. A few sources show a 11.2 mum feature with a peak position of similar to11.25 mum, a less steep blue rise, and a high tail-to-top ratio. The sources are classified independently on the basis of the 3.3 and 11.2 mum feature profiles and peak positions. Correlations between these classes and those based on the 6-9 mum features (Peeters et al.) are found. In particular, sources with the most common profiles in the 6-9 mum region also show the most common 3.3 and 11.2 mum feature profiles. However, the uncommon profiles do not correlate with each other. Also, these classifications depend on the type of object. In general, H II regions, nonisolated Herbig AeBe stars and young stellar objects show the same profiles for all 3-12 mum features. Many planetary nebulae and post-asymptotic giant branch stars show uncommon feature profiles. The three galaxies in our sample show the same profiles as the H II regions for all but the 11.2 mum feature, being similar to that of evolved stars. The observed pronounced contrast in the spectral variations for the CH modes (3.3 and 11.2 mum bands) versus the CC modes (6.2, 7.7, and 8.6 mum bands) is striking: the peak wavelengths of the features attributed to CC modes vary by similar to15-80 cm(-1), while for the CH modes the variations are similar to4-6.5 cm(-1). We summarize existing laboratory data and theoretical calculations of the modes emitting in the 3-12 mum region of PAH molecules and complexes. In contrast to the 6.2 and 7.7 mum components, which are attributed to PAH cations, the 3.3 mum feature appears to originate in neutral and/or negatively charged PAHs. We attribute the variations in peak position and profile of these IR emission features to the composition of the PAH family. The variations in FWHM of the 3.3 mum feature remains an enigma, while those of the 11.2 mum can be explained by anharmonicity and molecular structure. The possible origin of the observed contrast in profile variations between the CH modes and the CC modes is highlighted.