Simulations of long-term climatic variations require the use of coupled oceanic and atmospheric models. Given their different scales in space and time and present computing limitations, asynchronous coupling schemes are often used. Comparing the evolutions of simple dynamic systems which we couple alternatively with synchronous and asynchronous schemes, we show that the behaviour can be modified, not only in minute details, but drastically, if asynchronous coupling is used with insufficient care. We study how it happens, then suggest methods to insure that the average behaviour of more realistic models is not modified with asynchronous schemes. Other branches of physics with coupled non-linear systems could make use of these remarks.