A convoy of buses and cars carrying mostly foreign students left the northern city of Sumy, while dozens of people left Irpin near Kyiv.
Previous evacuations have failed, with Russia accused of shelling routes.
The UN says more than two million people have now fled Ukraine since Russia launched its invasion nearly two weeks ago.
Evacuations from Sumy began on Tuesday morning, with buses heading towards the city of Poltava, further south and away from the front line.
Indian and Chinese students were among those evacuated. The Indian government said all of its 694 students in the city had left with the convoy.
As he awaited evacuation, Mohammad Mahtab Raza, a 23-year-old medical student from India, told the BBC he had spent days sheltering from Russian strikes in a basement bunker.
“All my family call every day and ask: ‘When will you come back, what is your situation?’ Right now, with my mother and brother [I’m] just lying, [saying] ‘we are fine, everything is good, we will come really soon’,” he said.
Another medical student, 22-year-old Anastasia, was still weighing up whether to go.
“Now I’m deciding whether or not to leave my family, because [my] grandparents decided not to go and my mother cannot leave them, and now I need to decide to leave them alone, or to stay.”
In Sumy, the ceasefire appears to have largely held but other Ukrainian cities have continued to come under heavy bombardment from Russian forces.
Ukrainian officials said an evacuation route from Mariupol was being shelled in violation of the ceasefire agreement.
The Russian army “launched an attack right at the humanitarian corridor” and “did not let children, women and elderly people leave the city,” the defence ministry said on Facebook.
Meanwhile the situation in the city remains desperate.
One resident, Diana, told the BBC it was terrifying.
“It seemed to me like hell,” she said.
“Constant shelling above you, and at the same time, no electricity, no heat and no water. The coroner service cannot go and just pick [up] the bodies properly because of the shelling.
Residents have been leaving Irpin, north of Kyiv, many of them crossing a badly damaged bridge blown up to prevent a Russian advance.
“The city is almost ruined, and the district where I’m living, it’s like there are no houses which were not bombed,” a young mother told Reuters.
“As of 09:30 [07:30 GMT], more than 150 people have been evacuated and activities are under way [from Irpin],” said Kyiv Region Governor Oleksiy Kuleba, quoted by the agency.
Russia also says it has opened corridors from the cities of Chernihiv, Kharkiv and Kyiv, but Ukraine has not confirmed this.
Routes for corridors from Kyiv and Kharkiv announced by Russia on Monday were dismissed by Ukraine, as they led only to Belarus and Russia.
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