Dynasts lose their right to the throne if they marry without the permission of the monarch given in the Council of State. Individuals born to unmarried dynasts or to former dynasts that married without royal permission, and their descendants, are excluded from the throne. Further, when approving a marriage, the monarch can impose conditions that must be met in order for any resulting offspring to have succession rights. Part II, Section 9 of the Danish Constitution of 5 June 1953 provides that the parliament will elect a king and determine a new line of succession should a situation arise where there are no eligible descendants of King Christian X and Queen Alexandrine.
Before the 1953 Act of Succession, the throne passed by rules similar to Salic Law, however, unlike true Salic Law, the inheritance could pass through female lines, but a women herself could not take the throne. According to the 1853 Act of Succession, the throne passed to those descended from King Christian IX who was the grandfather of King Christian X.
The monarch in 1953, King Frederik IX, had three daughters but no sons. Under the 1853 act, the heir to the throne was Prince Knud, the King's younger brother. Prince Knud was far less popular than the King was. Further, Knud's mother-in-law, Princess Helena, was accused of supporting the Nazi movement during the Second World War. These factors, combined with a belief that the Salic Law was outdated, resulted in the movement to change the succession law so that Frederik's eldest daughter, the then Princess Margrethe, could inherit the throne.
Prince Knud had three children. Ingolf lost his rights to the throne in 1968 when he married without the monarch's permission. He was given the title Count of Rosenborg at that time. Similarly, Knud's younger son, Christian, lost his royal rights and became a Count of Rosenborg when he married without royal permission in 1971. In Denmark, those deprived of their rights to the throne also lose their royal rank and title. Count Ingolf and Count Christian are not to be referred to as princes except in an historical context from the period before they lost their rights. Only Knud's daughter, the unmarried Princess Elisabeth, retains her rights to the throne and the title "Princess of Denmark."
Queen Margrethe II's youngest sister, Princess Anne Marie, married King Constantine II of Greece in 1964. In view of the fact that she was marrying a foreign ruler, King Frederik IX decided that neither Anne Marie nor her children would have any right to the Danish throne. When the Queen's other sister, Princess Benedikte, married Prince Richard of Sayn-Wittgenstein-Berleburg in 1968, King Frederik IX decreed that her children would need to be raised in Denmark in order to have succession rights. Since the condition was not met, Princess Benedikte's three children do not have any right to the Danish throne. It is unclear (and probably irrelevant) whether her grandchildren and further issue will have succession rights if raised in Denmark.
Before 1953, various descendants of King Christian IX had succession rights in Denmark. The new Act of Succession terminated those rights but left the individuals involved in possession of their titles. This created a class of people with royal titles but no rights to the throne. As a distinction, those entitled to inherit the throne are called "Prins til Danmark" (Prince to Denmark, although this distinction is not made in English) while those without succession rights are referred to as "Prins af Danmark" (Prince of Denmark).
Although the Greek, Norwegian, and British Royal Families are genealogically part of the Danish Royal family, they are not descended from King Christian X and do not have any rights to the Danish throne. Norwegian Royals dropped all references to Denmark in their titles but Greek Royals continue to use the title "Prince(ss) of Greece and Denmark."
The Danish parliament has recently unanimously voted in favour of a new royal succession law that would allow a first-born child to one day ascend the throne regardless of whether it is a boy or a girl, similar to that of Sweden and Norway. Before it is adopted, the bill must also be voted through the next parliament, before finally being submitted to a referendum.