On Tuesday, the justices will weigh a California constitutional amendment banning same-sex unions, passed after gay marriage became legal there.
On Wednesday, a federal law defining marriage as between a man and a woman only, for the purpose of taxes and benefits, is up for review.
The court is expected to hand down its ruling by the end of June.
Outside the court in Washington DC, dozens of people have been queuing, some of them for several days, to secure a seat for the much-anticipated hearings.
Among those in court on Tuesday will be a lesbian cousin of Chief Justice John Roberts, the Los Angeles Times reports.California case
The first case will concern California's ban on same-sex marriages, known as Proposition 8, which was approved by that state's voters in a referendum in November 2008.
Recent opinion polls have shown rapid growth in US public support for gay marriageIts passage came only after some 18,000 gay marriages had already taken place in the state, following its legalisation of such unions earlier the same year.
Two same-sex couples filed a lawsuit, known as Hollingsworth v Perry, against Proposition 8.
As the state of California refused to defend it, the organisation that had sponsored Proposition 8 stepped in as defendants.
In 2010, a federal court ruled against Proposition 8, saying the state had not demonstrated a good reason for infringing on what the judge saw as a fundamental right for all couples to marry.
Supporters of the ban appealed against that ruling, but the court of appeals also said the amendment was unconstitutional.
Anti-gay marriage activists then petitioned the Supreme Court to review the case. They want the question of whether marriage should be defined as a union between a man and a woman to be left up to individual US states.
The Obama administration is not taking part in the case, but has filed what is called a "friend of the court" briefing, asking the Supreme Court to strike down the anti-gay marriage amendment.Inspecting the constitution
On Wednesday, the US Supreme Court will consider a federal law called the Defense of Marriage Act (Doma), which legally defines marriage as between a man and a woman.
A couple challenging Proposition 8 inspected the original US Constitution on the eve of the hearingUnder that law, same-sex couples are not eligible for federal benefits and tax breaks claimed by heterosexual couples.
Doma, signed in 1996 by former President Bill Clinton, has been overturned by four federal courts and two courts of appeal. They said the legislation unfairly discriminated against same-sex couples.
The lawsuit was triggered by New Yorker Edith Windsor, 83, who was required to pay $380,000 (£250,000) in federal estate taxes when her wife died in 2008. Heterosexual couples would be exempt from such taxes.
On Monday, the two couples involved in the Proposition 8 case visited the National Archives to inspect the original text of the US Constitution.
Their visit was to "reflect on the importance of their case for gay and lesbian couples across the nation", said the American Foundation for Equal Rights, which supports their case.
Overnight vigils have been planned across the country ahead of the hearings.
Currently, nine US states and the District of Columbia permit same-sex marriage. Eight other states allow civil unions or domestic partnerships with virtually all state marriage benefits, but do not allow couples to marry.
Recent opinion polls have shown a rapid growth in public support for the issue, and that most Americans now believe it should be legal.
The Supreme Court cases follow a flurry of declarations in support of gay marriage by high-profile figures, including last week by former Secretary of State Hillary Clinton.
Days earlier, Ohio's Rob Portman became the first Republican senator to back gay marriage.
And now three Democratic senators - Claire McCaskill of Missouri, Mark Warner of Virginia and Jay Rockefeller of West Virginia - have adopted the same stance.
