Being suggested by orthography, many Polish laymen – and, unfortunately, some linguistists too – think that the Polish language phonological system includes some nasal vowels, namely ę (nazal e), ą (not nasal a, but nasal o, written so for historical reasons) like those of French language. It was true maybe a century ago, but it is no longer; so-called nasal vowels have clearly nonsynchronous pronunciation, which means they are diphthongs (a vowel + semivowel) or simply sets of a vowel and a consonant.
The first segment is an oral or slightly nasalized (but this nasalization is not phonemically relevant) /ɔ/ or /ɛ/ and the second one depends on phonetic context; we will describe rules of this variation. What is interesting, those rules apply also to other Polish vowels, so if we talk about diphtong /ɔɰ̃/ in są (“(they) are”), there is also /iɰ̃/ in instytut (“institute”).
Before /p/ and /b/ the second segment is /m/: trąba /trɔmba/.
Before /t/, /d/, /t͡s/, /d͡z/, /t͡ʂ/, /d͡ʐ/ consonants it is /n/: wątroba /wɔntroba/.
Before /k/ and /g/ it is [ŋ]: bąk [bɔŋk].
Before /f/, /v/, /s/, /z/, /ʂ/, /ʐ/, /x/ and at the end of a word it is [ɰ̃]: są /sɔɰ̃/.
Before /d͡ʑ/ and /t͡ɕ/ it is /ɲ/:
Before /ɕ/ and /ʑ/ it is [j̃] or [ɰ̃]: gęś [gɛj̃ɕ] or [gɛɰ̃ɕ].