There are 2 cockroach species in the family Periplaneta on Madeira: Periplaneta americana and Periplaneta brunnea.
P. americana is lighter brown and the cerci (tail tips) are thinner than P. brunnea.
Despite the name, the American Cockroach (Periplaneta americana) is not endemic to the Americas. 
Periplaneta americana was introduced to the USA from Africa as early as 1625.
The American Cockroach has spread throughout the world by commerce.
It is found mainly in basements, sewers, steam tunnels, and drainage systems.
This cockroach is readily found in commercial and large buildings such as restaurants, grocery stores, bakeries, and anywhere food is prepared and stored.
They are now common in tropical climates.
They have an average length of around 4 cm.

I found it near a restaurant in Machico, Madeira, Portugal, 4 November 2013