The author announces some results on algebraic independence of the values of some classes of hypergeometric E-functions. Denote the hypergeometric E-function \[ \phi (z)=\sum^{\infty}_{n=0}\frac{[\lambda_ 3+1,n]^{k_ 3}}{[\lambda_ 1+1,n]^{k_ 1\quad}[\lambda_ 2+1,n]^{k_ 2}}(z/t)^{tn} \] satisfying certain conditions. If \(\lambda_ 1,\lambda_ 2\in {\mathbb{Q}}\setminus {\mathbb{Z}}\), \(\lambda_ 3\in {\mathbb{Z}}^+\) and the algebraic number \(\xi\in {\mathbb{A}}\setminus \{0\}\), then \(\phi (\xi),\phi '(\xi),...,\phi^{(t-1)}(\xi)\) are algebraically independent. The author also gives some results for general hypergeometric E-functions.