Dear Dr. Rapoport, dear co-authors,

Thank you for submitting your manuscript entitled “Model of Propagation of VLF Beams in the Waveguide Earth-Ionosphere” to Annales Geophysicae and for your response to the referee’s comments. I am very pleased to say that the manuscript is well written and interesting results are presented and discussed. However, as there have been sent by one of the referees some questions and suggestions with the best of intentions to improve the paper, the revision is requested. The referee is willing to read the improved version of the manuscript once again.
If you are prepared to undertake the improvements required, please submit the revised manuscript with indication of implemented changes.
Kindest regards
Yours sincerely
D. Buresova

Dear Dr. Rapoport, dear co-authors,

Thank you for your response to the referee’s comments. The constructive comments substantially helped improving the quality of the paper. The revised version confirms that you have made every attempt to accommodate the referee's comments and tried to address all of them satisfactorily. I am very pleased to say that recently the manuscript needs only some technical corrections. Please, read the manuscript carefully once more. There appeared some unclearness in the text. Most probably, some of them are due to conversion to pdf. format, e.g. “Ltym hf,jnf. C jndtnjv htwtyptynfv b ghb ‘njv enjxyz. B ntrcn” (lines 68-69) or references to the affiliations. The reviewer also refers to some unclearness in the second report attached below. Please, consider the technical comments and submit the final version of the manuscript.
Kindest regards

Yours sincerely
D. Buresova

The referee’s comments
The authors have considered my comments and the paper can be published. However I recommend to the authors to carefully read again their paper. I have seen some problems but I am not sure that I have seen all the small points concerning for example the equations and the figures.
Line 73 remove a in “adequately a data”
Line 430 Zc11 does not exist
There is a problem with the legend of Figure 3. We do not know where are the real and the imaginary parts of the components.
Line 443 -5 to be exponent
In Figure 6, 6b looks like 6f please check
Line 531 please check because it seems not related to fig 8d
Line 536 meaning of f here ? f is already used as the frequency !!