The effects of propaganda are analyzed in an opinion dynamics model in which, under certain conditions, individuals adjust their opinion as a result of random binary encounters. The aim of this paper is to study under what conditions propaganda changes the opinion dynamics of a social system. Four different scenarios are found, characterized by different sensitivities to the propaganda. For each scenario the maximum efficiency of propaganda is attained following a given strategy that is here outlined. Introduction.-The link between physics and sociology is historically profound. At the end of the XVII century, when G. Galilei and I. Newton gave birth to classical physics, philosophers proposed to apply similar deterministic laws to the broad fields of political and social sciences [1-3]. This idea was further strengthened by the discovery of universal demographic constants involving parameters strongly affected by individual free will or happenstance, such as the number of weddings, crimes and deaths [4]. The philosopher A. Comte, then introduced "social physics", a foundation of modern sociology which studies social dynamics using deter-ministic laws [5, 6]. As a typical social system is composed of a high number of individuals, statistics is the key tool for a quantitative study. Opinion dynamics is one of the fields of sociology that has interested physicists the most in the latest years. Opinion dynamics models can be divided into two large classes. The first class is represented by models based on binary opinions [7-11], in which social actors update their opinions as a result of social influence, often according to a kind of majority rule. The other class of opinion dynamics models considers the opinion as a continuous variable [12-17]. In this paper we focus on the latter and investigate the effect of propaganda. Indeed, we consider a model where agents adjust continuous opinions as a result of random binary encounters whenever their difference in opinion is below a given threshold [17]. This model is here termed Continuous Opinions with Threshold (COT) model and it is closely related to the "compromise model" studied in [18]. We are in particular interested in analyzing under what conditions propaganda affects the dynamics of the group's opinion. Here, propaganda is a "message" that touches every individual at the same time. The paper is organized as follows: first, we introduce the model and define the parameters involved. Then we show the results of the numerical simulations and compare them with dedicated analytical estimates. In conclusion, we will try to relate the mathematical results to actual social systems.