Order of disposition, Family Court, New York County (Jody Adams, J.), entered on or about May 11, 2005, which, upon a fact-finding determination that respondents mother and father neglected the subject children and that respondent father sexually abused Pearl M. and derivatively abused Evan M., placed the subject children in the custody of petitioner Administration for Children’s Services for a period of 12 months, unanimously affirmed insofar as it brings up for review the fact-finding determination, and the appeal otherwise dismissed as moot, without costs.

The appeal from the dispositional order is moot. The terms of the order have expired and subsequent orders terminating respondents’ parental rights freeing the children for adoption have been entered (Matter of Vivian OO., 34 AD3d 1084 [2006]; Matter of Clifford J., 238 AD2d 244 [1997]). Were we to review the merits, we would find that a preponderance of the evidence supported the determination that it was not in the best interests of the children to be returned to their parents.

The finding of neglect against respondent mother was supported by a preponderance of the evidence, including testimony and documentary proof establishing that she misused alcohol, failed to comply with a treatment program, and caused fires in the home, including one while the children were present (Family Ct Act § 1012 [f] [i] [B]). The finding of neglect against respondent father was established by evidence that he knew of the mother’s alcohol abuse and other dangerous tendencies, but failed to take steps to protect the children (see Matter of Kimberly M., 262 AD2d 237 [1999]).

The finding that the father sexually abused his daughter and derivatively abused his son was also supported by a preponder*349anee of the evidence (Family Ct Act § 1012 [e] [iii]; § 1046 [b] [i]). The daughter’s out-of-court statements were corroborated by a child sexual abuse expert, who, after evaluating the child over several sessions, concluded that she had been abused. Such corroboration included assessing the child’s demeanor and language and the consistency of her statements over time, as well the child’s demonstrations of the father’s actions with an anatomically correct doll (Matter of Jaclyn P., 86 NY2d 875 [1995], cert denied 516 US 1093 [1996]; Matter of J.S., 215 AD2d 213 [1995], lv denied 86 NY2d 706 [1995]). Contrary to the father’s contentions, he received adequate notice of the charges against him and his counsel was not curtailed during the cross-examination of petitioner’s key witness.

We have considered respondents’ remaining contentions and find them unavailing. Concur—Mazzarelli, J.P., Saxe, Sullivan, Catterson and Kavanagh, JJ.