Three studies compared bilinguals to monolinguals on 15 indicators of executive processing (EP). Most of the indicators compare a neutral or congruent baseline to a condition that should require EP. For each of the measures there was no main effect of group and a highly significant main effect of condition. The critical marker for a bilingual advantage, the Group × Condition interaction, was significant for only one indicator, but in a pattern indicative of a bilingual disadvantage. Tasks include antisaccade (Study 1), Simon (Studies 1–3), flanker (Study 3), and color-shape switching (Studies 1–3). The two groups performed identically on the Raven’s Advanced Matrices test (Study 3). Analyses on the combined data selecting subsets that are precisely matched on parent’s educational level or that include only highly fluent bilinguals reveal exactly the same pattern of results. A problem reconfirmed by the present study is that effects assumed to be indicators of a specific executive process in one task (e.g., inhibitory control in the flanker task) frequently do not predict individual differences in that same indicator on a related task (e.g., inhibitory control in the Simon task). The absence of consistent cross-task correlations undermines the interpretation that these are valid indicators of domain-general abilities. In a final discussion the underlying rationale for hypothesizing bilingual advantages in executive processing based on the special linguistic demands placed on bilinguals is interrogated.