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The subset  A  of the group  G  is called ( k ,  l )- sumset  if there exists subset  B  ⊆  G  such that  A  =  kB - lB , where  kB  -  lB  = { x  1  + ... +  x   k   -	 x   k +1  ... -  x   k + l   |  x  1 ,...,  x   k + l   ∈  B }. Upper and lower bounds of the number of ( k ,  l )-sumsets in the Abelian group are obtained.

Estimates of the number of ( k , l )-sumsets in the finite Abelian group