By Deepa Babington

PERUGIA, Italy (Reuters) - The family of British student Meredith Kercher said on Tuesday their ordeal would not end until they found out the truth about her murder, after Amanda Knox and her former boyfriend Raffaele Sollecito were acquitted by an Italian appeals court.

Stephanie Kercher, Meredith's sister, said they would first wait for the court's written explanation of Monday's verdict.

"Once we've got the reasons behind the decisions for this one, then we can understand why they have been acquitted of it and work toward finding those who are responsible," she told a news conference.

"That's the biggest disappointment, not knowing still and knowing that there is someone or people out there who have done this," she said.

The acquittal of Knox and Sollecito leaves Rudy Guede, an Ivorian drifter and drug dealer, as the only person convicted of the killing which investigators believe was committed by more than one person.

Kercher's body, with more than 40 wounds and a deep gash in her throat, was found in 2007 in the apartment she shared with U.S. student Knox in the Umbrian hill town of Perugia, where both were studying.

DNA evidence used to convict Knox and Sollecito was discredited by experts but questions remain over who, other than

Guede, was involved in the attack in which Kercher was pinned down and stabbed.

"I understand the courts agreed that he wasn't acting alone," Kercher's brother Lyle said.

"Of course if those released yesterday are not the guilty party, we are now obviously left wondering who is the other person or people.

"For us it feels very much like being back to square one. And the search goes on to find out what truly happened," he said.

Prosecutors say they will appeal against the acquittal verdict, which they say has left many issues relating to the murder unclear.

"I wasn't surprised but I was disturbed by it," prosecutor Manuela Comodi told reporters.

"It seems to me that all anyone's talked about, even before the trial began, was how the two accused were going to be acquitted."

The Kerchers have maintained a low profile throughout the trial. Knox's supporters ran a well-organized campaign to convince the wider public of her innocence.

The victim's family has refrained from any criticism of Knox or Sollecito but has said repeatedly that Meredith has been forgotten in the media frenzy over the young American.

"What happened to my daughter Meredith is every mother's nightmare," her Indian-born mother Arline said.

"We're still absorbing it. You think you've come to a decision and now it's been overturned."

British Prime Minister David Cameron urged people not to forget Meredith Kercher's family.

"Those parents ... had an explanation for what had happened to their wonderful daughter, and that explanation isn't there ... I think everyone should be thinking about them and how they feel," he told ITV.

(Writing By James Mackenzie; Editing by Janet Lawrence)