Maryland's Senate president, Mike Miller, says the Senate will begin debating the bill on Wednesday. Miller says the debate could last all day, and he says he has asked lawmakers to act "gentlemanlike" and "ladylike" as they consider the measure.
Miller says there could be a full vote on the bill next Tuesday.
It was approved by a Senate committee last week and has the stated support of 24 senators, which is the minimum needed for passage.
If approved, Maryland would become the sixth state to legalize gay marriage.