Citizenship of Guyana is based upon the Constitution of Guyana adopted in 1980

Dual citizenship is not recognized unless the second citizenship is obtained through marriage (US Mar. 2001, 89). The President may "by order" deprive an individual of Guyanese citizenship if he or she acquires the citizenship of another state in any other voluntary or formal manner (Guyana 20 Feb. 1980, Subs. 46(1)), or if he or she exercises any exclusive rights granted to citizens of another country which are voluntarily claimed and exercised in that other country (ibid., Subs. 46(2)).

Taken from http://www.refworld.org/docid/492ac7c9c.html

You cannot be denied the citizenship in the place of your birth for any reason. We do not practice exile or ostracism in the modern world. The Jagdeo regime wanted the right to do that and on that account decided on a residency criteria for Guyanese who are citizens elsewhere as well to be deemed eligible for political office. 

the idea of presidential authority to strip citizens of their birthright for procedural convenience is abject nonsense. This has to go. One has to voluntary request an abrogation of citizenship. The president should have no such authority.

Citizenship is not a simple and one-way issue.

A person can have more than one citizenship.

Note that if a person becomes a citizen of another country, there are specific circumstances when they have to renounce the citizenship of the former country to maintain the citizenship of the said country.

Note also that each country has its laws with regard to maintaining, renouncing, loosing, etc., citizenship.

Guyana Citizenship

GUYANA CITIZENSHIP: Citizenship is based upon the Constitution of Guyana, dated 1980.  Persons who were citizens of Guyana before the date of the Constitution remain citizens of Guyana.  Persons who were already spouses of these people are entitled to register as citizens of Guyana. (UKC-Commonwealth Nation)

• BY BIRTH: Child born after 1980 in the territory of Guyana, regardless of the nationality of the parents. The exception is a child born to parents who are diplomatic personnel, neither of whom is a citizen of Guyana.
• BY DESCENT: Child born abroad after 1980, either of whose parents is a native-born citizen of Guyana.
• MARRIAGE: Foreign citizen who marries a citizen of Guyana after 1980 is eligible to register for citizenship.
• BY NATURALIZATION: No information was provided.

GUYANA DUAL CITIZENSHIP:  NOT RECOGNIZED

Exception: The Constitution of 1980 states that any person who obtains the citizenship of another country after May 25, 1966 (except through marriage), shall lose their Guyanese citizenship. Questions concerning activities before this date should be directed to the Embassy.

GUYANA LOSS OF CITIZENSHIP:

• VOLUNTARY: Voluntary renunciation of Guyanese citizenship is permitted by law. Contact the Embassy for details and required paperwork.
• INVOLUNTARY: The following is grounds for involuntary loss of Guyanese citizenship: Person voluntarily acquires a foreign citizenship (except through marriage).

Source

Immigration TALK: Dual Citizenship

By Attorney Gail S. Seeram, June 26, 2011, By KNews, Filed Under News, Source

Dual citizenship refers to a person being a citizen of two countries at the same time. Persons may have dual nationality by automatic operation of different laws rather than by choice.

For example, a child born in a foreign country to U.S. citizen parents may be both a U.S. citizen and a citizen of the country of birth.

A person naturalized as a U.S. citizen may not lose the citizenship of their country of birth.  U.S. Law does not mention dual citizenship or require a person to choose one citizenship or another. Also, a person who is automatically granted another citizenship does not risk losing U.S. citizenship.

However, a person who acquires a foreign citizenship by applying for it may lose U.S. citizenship. In order to lose U.S. citizenship, the law requires that the person must apply for the foreign citizenship voluntarily, by free choice, and with the intention to give up U.S. citizenship.

The person’s statements or conduct can show intent.  The U.S. Government recognizes that dual citizenship exists but does not encourage it as a matter of policy because of the problems it may cause.

Claims of other countries on dual national U.S. citizens may conflict with U.S. law, and dual citizenship may limit U.S. Government efforts to assist citizens abroad. The country where a dual national is located generally has a stronger claim to that person’s allegiance.

However, dual citizens owe allegiance to both the United States and the foreign country. They are required to obey the laws of both countries. Either country has the right to enforce its laws, particularly if the person later travels there.

Most U.S. citizens, including dual nationals, must use a U.S. passport to enter and leave the United States.

Dual citizens may also be required by the foreign country to use its passport to enter and leave that country.

Use of the foreign passport does not endanger U.S. citizenship.  Most countries permit a person to renounce or otherwise lose citizenship.

Information on losing foreign citizenship can be obtained from the foreign country’s embassy and consulates in the United States.

Americans can renounce U.S. citizenship in the proper form at U.S. embassies and consulates abroad.

My brother and sister who were born in the UK applied for and received Guyanese passports.  

Not true, many nations does not recognize citizenship rights based on birth.

I have relatives whose kids were born in the US, Can and UK and received Guyana passports but to the birth of the parents.  Infact I was offered Guyana passports for my kids, if desired, due to us (parents) being born in Guyana.

So, I told my kids I will get it for them as long as they travel home and vote PPP.  They asked, who is PPP.

You need to buckle up with PPP propaganda and agitation in your household, baseman. You're doing party work on GNI but neglecting the home front.

i should have qualified that by saying if the parents are of the land as well.

Nah, all ok, party work is needed.

Correct, though not the case for many Hong Kong Indians, etc.