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A theory of nonlinear absorption of femtosecond light pulses by bulk crystals and nanostructures of differing dimensionality is developed. The pulse width is assumed to be small compared to the relaxation times of the electron and hole momenta. Expressions for the absorbed energy under conditions of multiphoton resonance are derived for transitions between discrete or band-related electron states and between sub-band states of size quantization in quantum wells and quantum wires. The dependence of the absorbed energy on the multiphoton resonance detuning and pulse width is analyzed. [ABSTRACT FROM AUTHOR]