They are a short lived perennial so the answer to your question is Yes I suppose.

But most people treat them as a biennial (sown this year - flower next year) because they are so easy to grow from seed.

Personally I will be pulling my plants out within the next few weeks and sowing seeds in the coldframe to plant out around October.

So the choice is yours!

However, there are some truly perennial (hardy) wallflowers - latin name 'Erysimum'. The most popular one is 'Bowles' Mauve'. They tend to get a bit 'woody' after a few years, but it's easy to take cuttings from them.

My favourite is called E. 'Constant Cheer'.