This article has three parts. In the first one, author examined the relationships between school composition and some characteristics of school process ('ethos' and school 'climate') according to Principal perceptions and students 'aggregated' perceptions, and their effects on mathematics achievement at the end of secondary education in Argentina. The study examined data from the Censo Nacional de Finalización del Nivel Secundario 1998 (High School National Census of 1998). Multilevel linear modeling with three levels (student, school and state) was used to analyze the school composition and process effects on achievement. It was found that (i) there are strong relationships between some composition and process variables; (ii) acting separately, both types of variables show strong effects on achievement, but (iii) the analyses of their jointly effect produces an important decline in the effect of composition and process school variables; (iv) while 'ethos' students variables (attitudes, expectations, academic self-concepts) maintain significant net effects on achievement, school 'climate' and other process variables from both students and Principal, are no longer effective predictors of achievement. In the second part, the analysis of some institutional process variables from the Director's questionnaire applied in the Operativo Nacional de Evaluación 2007 (National Assessment 2007) confirms some of the findings reported in the first part. Finally, the 1998 Census data are re-analyzed with multilevel models where classroom is specified as a level. The implications of the results in relation to the two previous parts are discussed.