The observations between the nth and (n + 1)th upper record value that fall in the interval X^U(n) - a , X^U(n)), where X^U(n) is upper record value and a > 0 is a constant, are called) the observations near the nth upper record value. In this paper, is obtained some stochastic orderings for number of observations near the nth upper and lower k-records based on different classes of life time distributions. Also, It is shown that only in exponential distribution is possible that the number of observations near the nth and mth upper k-record or lower .k-record be equal in distribution
