This kind of modality is realized in both 1anguages via modal verbs plus the infinitive of the notional verb, performing the function of compound modal verbal predicate.
1.1. Can / could.
Can / could expressing physical or mental ability is translated with the help of могти, вміти, мати змогу, можливість.
Не could hardly take his eyes off her - Нe міг очей відірвати від неї.
When expressing doubt, uncertainty - невже, хіба, навряд (mainly in interrogative and negative sentences) Can’t you believe me ? - Невже ви мені не вірите?
When expressing reproach, surprise, permission - можна. How can one promise that? - Як можна таке обіцяти?
In some environment can may be rendered in Ukrainian -through other modal verbs: How can you talk to me like that - Як ти смієш зі мною так розмовляти
Can / could followed by the perfect infinitive may be translated: through the past form of verb or through its subjunctive mood form. She can’t have neglected all that. - Невже вона всім цим знехтувала? Вона не могла всім цим знехтувати
N.B. Some modal meanings of can have no equivalents in Ukrainian I can hear you well. Я добре чую тебе. Can you see me? Ти бачиш мене?
1.2. May / might – to be permitted / to be allowed
expressing permission - можна. May I go? Можна йти?
expressing permission - дозволяти, не заперечувати
expressing possibility, assumption, uncertainty, advice - мати. І may remind him of a time he prefers to forget. Я матиму змогу пригадати йому той час, про який він воліє не згадувати.
When expressing wish - хай, щоб, initiating the sentences. May they live a long life - Хай їм щастить!
May / might followed by a perfect infinitive of actions which might not have been carried out. She may have forgotten... - Вона, мабуть, забула. Вона , певне, забула. Можливо, вона забула. Цілком імовірно, що вона забула. А ,може, вона забула...
Verb may is often used in the 1anguage of documents to express polite but severe warning: A member of the UNO... may be expelled from the organization. Держава - член ООН може бути виключена.