  A Skolem sequence of order n is a sequence S_n=(s_{1},s_{2},...,s_{2n}) of 2n
integers containing each of the integers 1,2,...,n exactly twice, such that two
occurrences of the integer j in {1,2,...,n} are separated by exactly j-1
integers. We prove that the necessary conditions are sufficient for existence
of two Skolem sequences of order n with 0,1,2,...,n-3 and n pairs in same
positions. Further, we apply this result to the fine structure of cyclic two,
three and four-fold triple systems, and also to the fine structure of
lambda-fold directed triple systems and lambda-fold Mendelsohn triple systems.
  For a better understanding of the paper we added more details into a
"Supplement".
