  Cyclic codes are an interesting type of linear codes and have wide
applications in communication and storage systems due to their efficient
encoding and decoding algorithms. Cyclic codes have been studied for many
years, but their weight distribution are known only for a few cases. In this
paper, let $\Bbb F_r$ be an extension of a finite field $\Bbb F_q$ and $r=q^m$,
we determine the weight distribution of the cyclic codes $\mathcal C=\{c(a, b):
a, b \in \Bbb F_r\},$ $$c(a, b)=(\mbox {Tr}_{r/q}(ag_1^0+bg_2^0), \ldots, \mbox
{Tr}_{r/q}(ag_1^{n-1}+bg_2^{n-1})), g_1, g_2\in \Bbb F_r,$$ in the following
two cases: (1) $\ord(g_1)=n, n|r-1$ and $g_2=1$; (2) $\ord(g_1)=n$,
$g_2=g_1^2$, $\ord(g_2)=\frac n 2$, $m=2$ and $\frac{2(r-1)}n|(q+1)$.
