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(1) Subject to the provisions of subsections (4), (5) and (7) of this section, no law shall make any provision that is discriminatory either of itself or in its effect.
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(3) In this section, the expression “discriminatory” means affording different treatment to different persons, attributable wholly or mainly to their respective descriptions by race, tribe, place of origin, political opinions, colour, creed or sex whereby persons of one such description are subjected to disabilities or restrictions to which persons of another such description are not made subject or are accorded privileges or advantages which are not accorded to persons of another such description.
(4) Subsection (1) of this section shall not apply to any law so far as that law makes provision-
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(c) with respect to adoption, marriage, divorce, burial, devolution of property on death or other matters of personal law;
(d) for the application in the case of members of a particular race, community or tribe of customary law with respect to any matter whether to the exclusion of any law in respect to that matter which is applicable in the case of other persons or not;
… (Sec. 15)

(1) This Constitution is the supreme law of Zimbabwe and any law, practice, custom or conduct inconsistent with it is invalid to the extent of the inconsistency.
… (Sec. 2)

The traditional and customary authorities are the guarantors of use and custom. (Art. 217)

In this Constitution—
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“Communal Land” means land set aside under an Act of Parliament and held in accordance with customary law by members of a community under the leadership of a Chief;
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“customary law” means the customary law of any section or community of Zimbabwe’s people;
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“traditional leader” means a person appointed as such in terms of section 283;
… (Sec. 332)

(1) The Swazi traditional government is administered according to Swazi law and custom and the traditional institutions that are pillars of the monarchy as set out in subsection (2).
(2) The following Swazi traditional institutions are hereby guaranteed and protected ...
(a) iNgwenyama;
(b) iNdlovukazi;
(c) Ligunqa (Princes of the Realm);
(d) Liqoqo;
(e) Sibaya;
(f) (Tikhulu) Chiefs;
(g) Umntfwanenkhosi Lomkhulu (Senior Prince);
(h) Tindvuna (Royal Governors). (Sec. 227)

The State shall safeguard the free exercise of the rites of religions and creeds in accordance with the customs observed in the Kingdom, if such is not inconsistent with public order or morality. (Art. 14)

(1) The President shall appoint a District Seyfo in consultation with the Minister responsible for Local Government.
(2) The Minister responsible for Local Government may, in consultation with the Regional Governors, make recommendations to the National assembly for the creation of new Seyfo Districts. (Sec. 58)

The State, subject to the provisions of this Constitution and national development policies and programs, shall protect the rights of indigenous cultural communities to their ancestral lands to ensure their economic, social, and cultural well-being.
The Congress may provide for the applicability of customary laws governing property rights or relations in determining the ownership and extent of ancestral domain. (Art. XII, Sec. 5)

1. Subject to the provisions of subsections (4) and (5) no law shall make any provision that is discriminatory either of itself or in its effect.
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3. In this section, the expression “discriminatory” means affording different treatment to different persons attributable wholly or mainly to their respective descriptions by race, colour, sex, language, religion, political or other opinion, national or social origin, property, birth or other status whereby persons of one such description are subjected to disabilities or restrictions to which persons of another such description are not made subject or are accorded privileges or advantages which are not accorded to persons of another such description.
4. Subsection (1) shall not apply to any law to the extent that that law makes provision—
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b. for the application, in the case of persons of any such description as is mentioned in subsection (3) (or of persons connected with such persons), of the law with respect to adoption, marriage, divorce, burial, devolution of property on death or other like matters which is the personal law of persons of that description;
c. for the application of the customary law of Lesotho with respect to any matter in the case of persons who, under that law, are subject to that law;
… (Sec. 18)

The State should promote and provide protection for different ethnic groups to have the right to live in the society according to the traditional culture, custom, and ways of life on a voluntary basis, peacefully and without interference, insofar as it is not contrary to public order or good morals or does not endanger the security of the State, health or sanitation. (Sec. 70)