We present a sequential procedure aimed at detecting reading acquisition difficulties. Data were collected from a representative sample (N=2012) of 2nd, 4th, and 6th graders from all state schools (n=14) and private schools (N=5) in a single district. In the first step, a silent reading test (Test de Eficiencia Lectora TECLE) was collectively conducted. It identified 273 children who presented reading difficulties that could not be explained by other causes (cognitive, sensory, behavioural, linguistic, and social). In the second step, the selected sample were administered a reading test (words and pseudo-words), and an orthographic test (words presenting inconsistent phoneme-to-grapheme items) to identify more basic phonological and orthographical deficits which might explain the reading difficulties detected using the Test de Eficiencia Lectora TECLE. The results showed a greater incidence of reading problems in 2nd-grade students (15.2%) than in 4th-grade (9.3%) and 6th-grade (10.9%) students. This difference could be explained by the presence of 2nd graders with reading difficulties who can overcome their difficulties without any special intervention. We also show that a large part of the global reading delay observed can be explained by difficulties in basic decoding and orthographic abilities.