Single-party states tend to arise during times of crisis; whether it's because of political instability, war, or an economic recession. Though the task of toppling the preceding regime is quite a hard task already, the task of establishing and maintaining power is arguably an even harder task. This is because once in power, the party or group that now rules has to quickly move to secure the power they now hold, because if they are left vulnerable, another overthrow is very likely. .
There are various ways in which single-party leaders of the past have managed to strengthen their power, but what is tantamount is the strengthening of their power domestically, which has proven to be the most vital item on the agendas of two of the twentieth century's most famous single-party leaders; Adolf Hitler and Mao Zedong. These two men, leaders of fascist Nazi Germany and Communist China respectively, both sought to make sure that within the borders of their nations, every citizen followed their rule. They consolidated their power by creating domestic policies which would in effect oppress the opposition, attract the masses, and also control their points of views.
Once in power, any single-party leader must find means to quiet down the opposition, as fears may grow of him being deposed. In Hitler's case in Nazi Germany, the Third Reich set up a "Terror State", which was comprised of the Gestapo, the SD (Sicherheitsdienst), and the SS (Schutzstaffel). In this Third Reich, The Decree for the Protection of People and State was issued and it allowed the indefinite arrest of people without trial. This was crucial to the Nazi regime because arrests were the most common form of oppression of the opposition. The SPD (Social Democratic Party) and the KPD (Communist Party) were two opposition groups in Germany that had the majority of the support of the working class, who made up 45% of the population.