The task of this paper is to investigate asymptotic behavior of segments of exponential series defined as $$ T_{\lambda}(x):=\sum_{n<\lambda x}\dfrac{c_n}{n!}x^n,\qquad \lambda\in R^+,\quad x\to\infty, $$ where $(c_n)_{n\in N}$ belongs to the set of regularly varying sequences in Karamata sense of arbitrary index. Precise results are obtained.