Luxembourg is described as a “full democracy”, with a parliamentary democracy headed by a constitutional monarch. Executive power is exercised by the grand duke and the cabinet, which consists of several other ministers.The Constitution of Luxembourg, the supreme law of Luxembourg, was adopted on 17 October 1868. The grand duke has the power to dissolve the legislature, in which case new elections must be held within three months. However, since 1919, sovereignty has resided with the nation, exercised by the grand duke in accordance with the Constitution and the law.

Legislative power is vested in the Chamber of Deputies, a unicameral legislature of sixty members, who are directly elected to five-year terms from four constituencies. A second body, the Council of State (Conseil d’État), composed of twenty-one ordinary citizens appointed by the grand duke, advises the Chamber of Deputies in the drafting of legislation.
https://en.wikipedia.org/wiki/Luxembourg