Deaf people have different sign languages in each country. Just as English is different from Spanish, international sign languages vary in syntax, grammar, and concepts. We have Ethiopian sign languages, Brazilian Sign Language, Chinese Sign Language, Austrian Sign Language and British Sign Language, etc but I am going to mention few so that you can have a better idea of what they are.

AMERICAN SIGN LANGUAGE (ASL) uses signs, gestures, specific facial expressions, non-manual movements, and the like to express feelings, ideas, and concepts visually. It uses no voice, but does have facial grammar (non-manual markers, mouth morphemes). It uses a completely
different grammar system and sentence structure as that of spoken English. The rules of grammar, which will be discussed in a different section of this site, are clear and developed.

SIGNED EXACT ENGLISH (SEE) the ideas behind these systems is that Deaf and Hard of Hearing children will learn English better if they are exposed, visually through signs, to the grammatical features of English. The base signs are borrowed from ASL, but the various inflections are not used. A lot of initialization is used. Additionally, a lot of “grammatical markers” for numbers, person, tense, etc., are added, and strict English word order is used. Every prefix, suffix, article, conjunction, auxiliary verb, etc., is signed. Also, English homophones are represented by identical signs (i.e. the same sign is used for the noun fish and the verb fish, which have different ASL signs).

LINGUISTICS OF VISUAL ENGLISH (L.O.V.E.) Developed by Dennis Wampler. It has similarities to Signed Exact English. It is a signing system rather than language on its own. Therefore some people claim that exposure to L.O.V.E. does not provide children with the complete linguistic access that is needed to internalize whole language.

NIGERIAN SIGN LANGUAGE (NSL) it is the national sign language of deaf people in Nigeria. It was introduced in 1960, a few years after Ghanaian Sign Language, by Andrew Foster, a deaf African-American missionary. It is the combined of both American Sign Language and Signed Exact English. NSL is unrelated to local Nigerian sign languages such as Hausa Sign Language, Yoruba Sign Language, and Igbo Sign Language.

The problem with the English-based sign language systems is that they are very slow. They are easier to learn for hearing people than ASL, but they are slower to use, because, on average, signs take twice as long as words to produce. So the average proposition takes twice as long to express. Also, you have to be grammatically very self-aware to use them. The research shows that most parents and many teachers who are trying to use these systems, end up leaving out many of the grammatical markers and that many children exposed to them end up modifying them to more ASL-like forms.

Culled from Cheeta's blog:

The Sign Language System