According to Wikipedia, Italian is spoken to some degree in Libya, Eritrea and Federal Republic of Somalia.
Are there in Africa any clearly different varieties of this language which have distinct local traits?
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The only Italian colony with any substantial settlement was Libya which mostly occurred in the 1930s. Just before WWII over 100,000 or 1/8 of the inhabitants were Italian settlers, or Italo-Libyans, many of whom left during and after the war. A common estimate for 1962 is 35.000 Italians in Libya. They were ordered to leave after al-Gaddafi took power, though it seems there was still some 1,500 in the country by 1982.
There was simply no time for a Libyan Italian dialect to evolve.