In this paper, for an analytic function f(s) in the half-plane Re s < a, which is of irregu- lar growth, it is shown that lower type is aiv. ays zero and, therefore; to study precisely the growth of such analytic functions, the concept of X-type has been introduced and then some relations which connect k-type with the maximum terin, have been obtaıned. İn the last, formula for X-type in terms of coefficients and exponeııts in Dirichlet series expansion for f(s) has been ob- tained.