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<jats:title>ABSTRACT</jats:title> <jats:p>We report the results from a comprehensive study of 74 ultraluminous infrared galaxies (ULIRGs) and 34 Palomar-Green (PG) quasars within <jats:italic>z</jats:italic> ∼ 0.3 observed with the <jats:italic>Spitzer</jats:italic> Infrared Spectrograph (IRS). The contribution of nuclear activity to the bolometric luminosity in these systems is quantified using six independent methods that span a range in wavelength and give consistent results within ∼±10%–15% on average. This agreement suggests that deeply buried active galactic nuclei (AGNs) invisible to <jats:italic>Spitzer</jats:italic> IRS but bright in the far-infrared are not common in this sample. The average derived AGN contribution in ULIRGs is ∼35%–40%, ranging from ∼15%–35% among “cool” (<jats:italic>f</jats:italic> <jats:sub>25</jats:sub>/<jats:italic>f</jats:italic> <jats:sub>60</jats:sub> ⩽ 0.2) optically classified H <jats:sc>ii</jats:sc>-like and LINER ULIRGs to ∼50 and ∼75% among warm Seyfert 2 and Seyfert 1 ULIRGs, respectively. This number exceeds ∼80% in PG QSOs. ULIRGs fall in one of three distinct AGN classes: (1) objects with small extinctions and large polycyclic aromatic hydrocarbon (PAH) equivalent widths are highly starburst-dominated; (2) systems with large extinctions and modest PAH equivalent widths have larger AGN contributions, but still tend to be starburst-dominated; and (3) ULIRGs with both small extinctions and small PAH equivalent widths host AGN that are at least as powerful as the starbursts. The AGN contributions in class 2 ULIRGs are more uncertain than in the other objects, and we cannot formally rule out the possibility that these objects represent a physically distinct type of ULIRGs. A morphological trend is seen along the sequence (1)–(2)–(3), in general agreement with the standard ULIRG−QSO evolution scenario and suggestive of a broad peak in extinction during the intermediate stages of merger evolution. However, the scatter in this sequence, including the presence of a significant number of AGN-dominated systems prior to coalescence and starburst-dominated but fully merged systems, implies that black hole accretion, in addition to depending on the merger phase, also has a strong chaotic/random component, as in local AGNs.</jats:p>