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In agglutinative languages there are normally roots for nouns and/or verbs that can have multiple morphemes attached as affixes, following certain rules, to add information such as tense, aspect, mood, person, number, etc.

There is a lot of diversity among agglutinative languages, some agglutinate several word classes, other languages only one word class. Each language has its own rules with the affixes usually (but not always) fitting a "template" of which affixes come in which position / order.

But have linguistic universals of these morphemes been studied to see common tendencies of the ordering of the morphemes across languages?

I would expect some trends and maybe big differences between suffixing and prefixing languages, but it's only a hunch and I don't know where to look.

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    If I recall from my typology book there is a universal consensus order to verb affixes/phrases that occurs regardless of whether the language is agglutinative or isolating: verb, voice, aspect, tense, mood, agreement (or the opposite as the language may be). For nouns its: noun, number, case (or, again, exactly the opposite).
    – Justin Olbrantz
    Apr 26, 2014 at 7:10
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    Key words: "complexity-based ordering" (Jennifer Hay and Ingo Plag, among many others).
    – Alex B.
    May 26, 2014 at 2:07

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I think one of the first major studies was Bybee (1985).

Bybee, J.L. 1985. Morphology: A study of the relation between meaning and form. Amsterdam: John Benjamins Publishing Company.

She proposed the hierarchy Justin Olbranz refers to: 

verb-valence-voice-aspect-tense-mood-modality-person-number

Another prominent study that argues along the same line is Rice (2000):

Rice, Keren. 2000. Morpheme order and semantic scope: Word formation in the Athapaskan verb. Cambridge: Cambridge University Press.

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Not to refute tendencies in morpheme ordering, but for a different take on your question, this paper discusses how ordering can be compositionally driven by scope, based on data from a very agglutinating polysynthetic language Adyghe (Northwest Caucasian).

Adyghe affixes are often described in templatic terms, but the authors show it's not universally true in this language. Rather, ordering is often not fixed but determined by semantics. For example, different orderings of the simulative and habilitive suffixes allows to get different interpretations, as in (1) vs. (2):

(1) He can [pretend [as if he's taking a star from the sky]].

(2) He pretends [he can [take a star from the sky]].

The authors propose that an affix sits next to its scope, and that scopal morphology is compositional.

Recently there's been a paper that argues, based on Yi (Tibeto-Burman) data, that scopal morphology is not necessarily compositional. The author supports it with opaque morpheme combinations and cases where only one scope can obtain between two morphemes.

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    Thanks for your answer! Do you think you can expand it and give a brief explanation of how the content of these papers reflects on the question, so that readers get a more specific idea of their relevance?
    – robert
    May 18, 2014 at 21:59
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    Sure, did that.
    – Ivan Kapitonov
    May 25, 2014 at 16:57
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    @Ivan Yes, that. And it's likely that in languages with strict morpheme ordering the ordering developed based on scope.
    – Justin Olbrantz
    May 25, 2014 at 21:12
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Your best bet for looking at universals is the Universals Archive of the University of Konstanz. If you go under the search tab, you'll find options to narrow down what you're looking for. I suggest either morphology or inflection as the search domain.

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