<PAGE>   1

Exhibit 10 (af)
                          [NCT Group, Inc. letterhead]


December 1, 1999



Atlantis Capital Fund
c/o Thomson Kernaghan & Co., Ltd.
465 Bay Street, 10th Floor
Toronto, Ontario, Canada  M5H 2V2

                 Letter Agreement Relating to and Modifying the
             Certificate of Designations, Preferences and Rights of
                     Series F Convertible Preferred Stock of
                                 NCT Group, Inc.


Gentlemen:

Reference is made to that certain Certificate of Designations, Preferences and
Rights of Series F Convertible Preferred Stock of NCT Group, Inc. (the
"Certificate of Designations"), whereby NCT Group, Inc., a Delaware corporation
(the "Company") established and set forth the powers, designations, preferences
and relative, participating, optional or other special rights and
qualifications, limitations or restrictions of its Series F Convertible
Preferred Stock (the "Series F Preferred Stock").

The Company acknowledges that it entered into the Securities Purchase Agreement,
dated as of August 6, 1999 (the "Purchase Agreement"), with each investor
listed on the Schedule of Buyers attached thereto (each, a "Buyer" and
collectively, the "Buyers"), pursuant to which the Company agreed to sell to
the Buyers, and the Buyers agreed to purchase, an aggregate amount of up to
Twelve Thousand Five Hundred (12,500) shares of the Series F Preferred Stock,
in accordance with the terms and conditions of the Certificate of Designations
filed by the Company with the Secretary of State of the State of Delaware on
September 8, 1999. The Company further acknowledges that it may exceed the
Maximum Share Issuance Amount, as that term is defined in Section 4(b) of the
Certificate of Designations, and, as such, would be obligated to immediately
notify Buyers and redeem all of the remaining shares of Series F Preferred
Stock then outstanding in accordance with the terms and conditions of Section
4(k) of the Certificate of Designations. Accordingly, the Company desires to
amend the Certificate of Designations, and the Buyers desire to consent to such
amendment, in accordance with the terms of this letter agreement (the "Letter
Agreement").

In order to facilitate the conversion of the outstanding shares of Series F
Preferred Stock into fully authorized and issued shares of common stock of the
Company, the Buyers hereby consent to the amendment of the Certificate of
Designations to increase the Maximum Share Issuance

                                                                           116
<PAGE>   2

Amount from Thirty-five Million (35,000,000) shares of common stock of the
Company to Seventy-seven Million (77,000,000) shares of common stock of the
Company.

If you are in agreement with the foregoing, please execute this Letter
Agreement in the space provided below.


                                                     NCT GROUP, INC.


                                                     By: _____________________
                                                         Name:
                                                         Title:


Acknowledged and agreed to as of the date first written above:

ATLANTIS CAPITAL FUND

By: __________________________
    Name:
    Title:



                                                                           117

<PAGE>   3

                          [NCT Group, Inc. letterhead]

December 1, 1999



Canadian Advantage Limited Partnership
c/o Thomson Kernaghan & Co., Ltd.
465 Bay Street, 10th Floor
Toronto, Ontario, Canada  M5H 2V2

                 Letter Agreement Relating to and Modifying the
             Certificate of Designations, Preferences and Rights of
                     Series F Convertible Preferred Stock of
                                 NCT Group, Inc.


Gentlemen:

Reference is made to that certain Certificate of Designations, Preferences and
Rights of Series F Convertible Preferred Stock of NCT Group, Inc. (the
"Certificate of Designations"), whereby NCT Group, Inc., a Delaware corporation
(the "Company") established and set forth the powers, designations, preferences
and relative, participating, optional or other special rights and
qualifications, limitations or restrictions of its Series F Convertible
Preferred Stock (the "Series F Preferred Stock").

The Company acknowledges that it entered into the Securities Purchase Agreement,
dated as of August 6, 1999 (the "Purchase Agreement"), with each investor
listed on the Schedule of Buyers attached thereto (each, a "Buyer" and
collectively, the "Buyers"), pursuant to which the Company agreed to sell to
the Buyers, and the Buyers agreed to purchase, an aggregate amount of up to
Twelve Thousand Five Hundred (12,500) shares of the Series F Preferred Stock,
in accordance with the terms and conditions of the Certificate of Designations
filed by the Company with the Secretary of State of the State of Delaware on
September 8, 1999. The Company further acknowledges that it may exceed the
Maximum Share Issuance Amount, as that term is defined in Section 4(b) of the
Certificate of Designations, and, as such, would be obligated to immediately
notify Buyers and redeem all of the remaining shares of Series F Preferred
Stock then outstanding in accordance with the terms and conditions of Section
4(k) of the Certificate of Designations. Accordingly, the Company desires to
amend the Certificate of Designations, and the Buyers desire to consent to such
amendment, in accordance with the terms of this letter agreement (the "Letter
Agreement").

In order to facilitate the conversion of the outstanding shares of Series F
Preferred Stock into fully authorized and issued shares of common stock of the
Company, the Buyers hereby consent to the amendment of the Certificate of
Designations to increase the Maximum Share Issuance Amount from Thirty-five
Million (35,000,000) shares of common stock of the Company to Seventy-seven
Million (77,000,000) shares of common stock of the Company.
                                                                           118
<PAGE>   4

If you are in agreement with the foregoing, please execute this Letter
Agreement in the space provided below.


                                                     NCT GROUP, INC.


                                                     By: _____________________
                                                         Name:
                                                         Title:


Acknowledged and agreed to as of the date first written above:

CANADIAN ADVANTAGE LIMITED PARTNERSHIP

By: __________________________
    Name:
    Title:


                                                                           119

<PAGE>   5


                          [NCT Group, Inc. letterhead]

December 1, 1999



Dominion Capital Fund, Ltd.
c/o Thomson Kernaghan & Co., Ltd.
465 Bay Street, 10th Floor
Toronto, Ontario, Canada  M5H 2V2

                 Letter Agreement Relating to and Modifying the
             Certificate of Designations, Preferences and Rights of
                     Series F Convertible Preferred Stock of
                                 NCT Group, Inc.


Gentlemen:

Reference is made to that certain Certificate of Designations, Preferences and
Rights of Series F Convertible Preferred Stock of NCT Group, Inc. (the
"Certificate of Designations"), whereby NCT Group, Inc., a Delaware corporation
(the "Company") established and set forth the powers, designations, preferences
and relative, participating, optional or other special rights and
qualifications, limitations or restrictions of its Series F Convertible
Preferred Stock (the "Series F Preferred Stock").

The Company acknowledges that it entered into the Securities Purchase Agreement
dated as of August 6, 1999 (the "Purchase Agreement"), with each investor
listed on the Schedule of Buyers attached thereto (each, a "Buyer" and
collectively, the "Buyers"), pursuant to which the Company agreed to sell to
the Buyers, and the Buyers agreed to purchase, an aggregate amount of up to
Twelve Thousand Five Hundred (12,500) shares of the Series F Preferred Stock,
in accordance with the terms and conditions of the Certificate of Designations
filed by the Company with the Secretary of State of the State of Delaware on
September 8, 1999. The Company further acknowledges that it may exceed the
Maximum Share Issuance Amount, as that term is defined in Section 4(b) of the
Certificate of Designations, and, as such, would be obligated to immediately
notify Buyers and redeem all of the remaining shares of Series F Preferred
Stock then outstanding in accordance with the terms and conditions of Section
4(k) of the Certificate of Designations. Accordingly, the Company desires to
amend the Certificate of Designations, and the Buyers desire to consent to such
amendment, in accordance with the terms of this letter agreement (the "Letter
Agreement").

In order to facilitate the conversion of the outstanding shares of Series F
Preferred Stock into fully authorized and issued shares of common stock of the
Company, the Buyers hereby consent to the amendment of the Certificate of
Designations to increase the Maximum Share Issuance Amount from Thirty-five
Million (35,000,000) shares of common stock of the Company to Seventy-seven
Million (77,000,000) shares of common stock of the Company.

                                                                           120
<PAGE>   6

If you are in agreement with the foregoing, please execute this Letter Agreement
in the space provided below.


                                                     NCT GROUP, INC.


                                                     By:  ____________________
                                                          Name:
                                                          Title:


Acknowledged and agreed to as of the date first written above:

DOMINION CAPITAL FUND, LTD.

By:      /s/ DAVID SIMS
         ----------------
         Name: David Sims
         Title:


                                                                           121

<PAGE>   7

                          [NCT Group, Inc. letterhead]

December 1, 1999



Endeavour Capital Fund S.A.
Attn.:  Shmuli Margulies
14/14 Divrei Chaim Street
Jerusalem  94479  Israel

                 Letter Agreement Relating to and Modifying the
             Certificate of Designations, Preferences and Rights of
                     Series F Convertible Preferred Stock of
                                 NCT Group, Inc.


Gentlemen:

Reference is made to that certain Certificate of Designations, Preferences and
Rights of Series F Convertible Preferred Stock of NCT Group, Inc. (the
"Certificate of Designations"), whereby NCT Group, Inc., a Delaware corporation
(the "Company") established and set forth the powers, designations, preferences
and relative, participating, optional or other special rights and
qualifications, limitations or restrictions of its Series F Convertible
Preferred Stock (the "Series F Preferred Stock").

The Company acknowledges that it entered into the Securities Purchase Agreement,
dated as of August 6, 1999 (the "Purchase Agreement"), with each investor listed
on the Schedule of Buyers attached thereto (each, a "Buyer" and collectively,
the "Buyers"), pursuant to which the Company agreed to sell to the Buyers, and
the Buyers agreed to purchase, an aggregate amount of up to Twelve Thousand
Five Hundred (12,500) shares of the Series F Preferred Stock, in accordance
with the terms and conditions of the Certificate of Designations filed by the
Company with the Secretary of State of the State of Delaware on September 8,
1999. The Company further acknowledges that it may exceed the Maximum Share
Issuance Amount, as that term is defined in Section 4(b) of the Certificate of
Designations, and, as such, would be obligated to immediately notify Buyers and
redeem all of the remaining shares of Series F Preferred Stock then outstanding
in accordance with the terms and conditions of Section 4(k) of the Certificate
of Designations. Accordingly, the Company desires to amend the Certificate of
Designations, and the Buyers desire to consent to such amendment, in accordance
with the terms of this letter agreement (the "Letter Agreement").

In order to facilitate the conversion of the outstanding shares of Series F
Preferred Stock into fully authorized and issued shares of common stock of the
Company, the Buyers hereby consent to the amendment of the Certificate of
Designations to increase the Maximum Share Issuance Amount from Thirty-five
Million (35,000,000) shares of common stock of the Company to Seventy-seven
Million (77,000,000) shares of common stock of the Company.
                                                                           122
<PAGE>   8

If you are in agreement with the foregoing, please execute this Letter
Agreement in the space provided below.


                                                     NCT GROUP, INC.


                                                     By:  ____________________
                                                          Name:
                                                          Title:


Acknowledged and agreed to as of the date first written above:

ENDEAVOUR CAPITAL FUND S.A.

By: /s/ SHMULI MARGULIES
    -----------------------
    Name: Shmuli Margulies
    Title:


                                                                           123

<PAGE>   9

                          [NCT Group, Inc. letterhead]

December 1, 1999



Sovereign Partners, L.P.
c/o Thomson Kernaghan & Co., Ltd.
465 Bay Street, 10th Floor
Toronto, Ontario, Canada  M5H 2V2

                 Letter Agreement Relating to and Modifying the
             Certificate of Designations, Preferences and Rights of
                     Series F Convertible Preferred Stock of
                                 NCT Group, Inc.


Gentlemen:

Reference is made to that certain Certificate of Designations, Preferences and
Rights of Series F Convertible Preferred Stock of NCT Group, Inc. (the
"Certificate of Designations"), whereby NCT Group, Inc., a Delaware corporation
(the "Company") established and set forth the powers, designations, preferences
and relative, participating, optional or other special rights and
qualifications, limitations or restrictions of its Series F Convertible
Preferred Stock (the "Series F Preferred Stock").

The Company acknowledges that it entered into the Securities Purchase
Agreement, dated as of August 6, 1999 (the "Purchase Agreement"), with each
investor listed on the Schedule of Buyers attached thereto (each, a "Buyer" and
collectively, the "Buyers"), pursuant to which the Company agreed to sell to
the Buyers, and the Buyers agreed to purchase, an aggregate amount of up to
Twelve Thousand Five Hundred (12,500) shares of the Series F Preferred Stock,
in accordance with the terms and conditions of the Certificate of Designations
filed by the Company with the Secretary of State of the State of Delaware on
September 8, 1999. The Company further acknowledges that it may exceed the
Maximum Share Issuance Amount, as that term is defined in Section 4(b) of the
Certificate of Designations, and, as such, would be obligated to immediately
notify Buyers and redeem all of the remaining shares of Series F Preferred
Stock then outstanding in accordance with the terms and conditions of Section
4(k) of the Certificate of Designations. Accordingly, the Company desires to
amend the Certificate of Designations, and the Buyers desire to consent to such
amendment, in accordance with the terms of this letter agreement (the "Letter
Agreement").

In order to facilitate the conversion of the outstanding shares of Series F
Preferred Stock into fully authorized and issued shares of common stock of the
Company, the Buyers hereby consent to the amendment of the Certificate of
Designations to increase the Maximum Share Issuance Amount from Thirty-five
Million (35,000,000) shares of common stock of the Company to Seventy-seven
Million (77,000,000) shares of common stock of the Company.

                                                                           124
<PAGE>   10

If you are in agreement with the foregoing, please execute this Letter
Agreement in the space provided below.


                                                     NCT GROUP, INC.


                                                     By:  ____________________
                                                          Name:
                                                          Title:


Acknowledged and agreed to as of the date first written above:

SOVEREIGN PARTNERS, L.P.

By:  /s/ STEVE HICKS
     ---------------
     Name: Steve Hicks
     Title:


                                                                           125