Earlier this month, it was reported that the Manchester United football star had had secret dates with Page Three model Emma Ryan, 23.
The trysts are said to have taken place while Ms Adams, 24, who is five months pregnant with Beckham's baby, was away on the Spice Girls' world tour and ended when she returned from America.
In another report, it was alleged that Beckham, 23, was still "in touch" with a former girlfriend.
Speaking for the first time about the reports, Ms Adams told the Daily Mail: "I trust David 110%. I've found the person I want to spend the rest of my life with.
"These stories are so ludicrous that we are going to take legal action.
"The truth is we are stronger than ever and both looking forward to having the baby. The reports haven't damaged our relationship at all.
"The only thing that matters is that we love and trust each other and our families are okay.
"If people want to believe what they are reading, that's up to them."
Posh and Beckham announced their engagement in January but said they would get married until the summer of next year.
The Spice Girls are currently working on their third album - their first without Ginger Spice Geri Halliwell.
Posh Spice and Beckham overjoyed at baby news
(22 Aug 98 | Entertainment)
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