They were arrested two years ago, days after Canada detained the daughter of the founder of telecom giant Huawei on the request of the US.
Monday's trial is being held behind closed doors and no immediate verdict is expected.
Mr Kovrig is a former diplomat and has worked for the International Crisis Group think tank while Michael Spavor was a businessman.
They have been in prison since their arrests in 2018 and face lengthy jail terms if found guilty.
The arrests have frayed relations between the two countries and Ottawa has accused Beijing of "hostage diplomacy".
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