Marxism and Critical theory

Critical theorists, such as Max Horkheimer, Theodor Adorno, Herbert Marcuse and Jurgen Habermas, aimed to understand and uncover the assumptions that keep us from a full and true understanding of how the world works. Their based their theories on Hegel's and Marx's views but how did these, first and second generation critical theorists, of the Frankfurt school, attempt to improve upon the limitations of their Marxist orthodox ancestors?