Females are known to excel over males in most reading tasks, but not consistently so in tasks that require processing information from maps, tables, charts and diagrams, so called `Documents'. The IEA Reading Literacy data provides possibilities to investigate gender differences across countries in such tasks in two age groups, 9-year-olds and 14-year-olds. The general question about cultural influences vs. an invariant pattern of gender differences is of great interest for gender research, and central in this study. The aim of the paper is to describe and analyze gender differences on Document tasks, and investigate if and how the pattern of differences varies over countries. Another aim is to demonstrate the power of using a multivariate analysis technique by contrasting it against traditional univariate approaches. The univariate analysis indicates female advantage as the most common in the younger group and a mixed pattern in the older. The multivariate analysis indicate that Document tasks are not unidimensional, because both general and specific dimensions can be extracted from the raw scores. The traditional univariate analysis often disguised true patterns of differences in the data, both in terms of country differences and in terms of the direction of the gender differences. Raw score differences between the genders proved to be due to differences in both general and passage specific dimensions. Ten of the countries showed gender differences in both directions in the general dimension among 9-year-olds, while an almost consistent pattern of female advantage was found among 14-years-olds. Many of the specific passage dimensions turned out to favor either males or females. This complex pattern varied over both age groups and across countries, although commonalities in the pattern among subgroups of countries were common.