You could also create an unnamed query
    db.createquerydef ("",strSQL) which will not persist after the procedure
and thus you do not have to worry about deleting it.

You could also loop through the querydefs checking for the queryname or trap
the error by trying to set the new querydef ti the same name, but the above
is simplest and most effecient.
Hope this helps,
GR

   Set MyDB = DBEngine.Workspaces(0).Databases(0)

    ' Check if Query exists, delete if it does
    If (IsNull(MyDB.QueryDefs("sql_Search").Name) = False) Then
        DoCmd.DeleteObject A_QUERY, "sql_Search"
    End If

    Set myquery = MyDB.CreateQueryDef("sql_Search", sql_report)

HTH
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1) iterate through the Table documents collection
2) iterate through the Querydefs collection
3) check for the query in the Msysobjects table

Number 1 is the least efficient
Number 2 goes like this

Function DoesQueryExist(QueryName As String) As Boolean
  Dim lodb As Database
  Dim loqdf As QueryDef
  Dim blnRet As Boolean
  blnRet = False
  Set lodb = CurrentDb
  For Each loqdf In lodb.QueryDefs
    If loqdf.Name = QueryName Then
      blnRet = True
      Exit For
    End If
  Next
  DoesQueryExist = blnRet
End Function

Number 3 goes like this

Function DoesQueryExist(QueryName As String) As Boolean
  Dim lodb As Database
  Dim strsql As String
  Dim lorst As Recordset
  strsql = "select count(name) as CountOfName " _
         & "from msysobjects " _
         & "where name = '" & QueryName & "' and type = 5"
  Set lodb = CurrentDb
  Set lorst = lodb.OpenRecordset(strsql)
  DoesQueryExist = CBool(lorst!CountOfName)
End Function