The Australian Stock Exchange has a good number of fantastic growth shares. With the likes of SEEK Limited (ASX: SEK) and REA Group Limited (ASX: REA) to choose from, it is incredibly hard to choose my two favourites.

But after a lot of thought, I have decided that the following two companies are my favourite growth shares on the S&P/ASX 200 (Index: ^AXJO) (ASX: XJO) at present.

Domino’s Pizza Enterprises Ltd. (ASX: DMP)

In the last five years the shares of Domino’s may have risen by almost 750%, but there is still a great deal more growth ahead for this quick service restaurant king.

I believe Domino’s focus on technology has really given it an advantage over its competitors. The ease at which consumers can order pizza and track its progress online or on their phones is fantastic.

This should help the company compete with fast food giants McDonalds and KFC. Especially when it goes head to head with them in the near future. As you may have noticed it has dropped the word “Pizza” from the company name as part of its plan to offer more than just pizza.

If the company can make a success of its venture into other food items, I see little reason why it cannot continue to grow its earnings at the high rate it has previously.

Domino’s has produced earnings growth of 24% per annum for the last five years. According to CommSec, analysts have forecast this to ramp up to 33% per annum for the next couple of years. This seems very achievable in my opinion and justifies the shares trading at 55 times estimated forward earnings.

As long as Domino’s can continue to produce strong results, I believe investors will be happy to pay a premium to hold the shares. However if growth were to slow, investors should be mindful of potential steep declines in the share price.

Premier Investments Limited (ASX: PMV)

Premier Investments is my other favourite growth share on the ASX currently. It has delivered a great year so far thanks to the strong performance of its hugely popular retail brands such as Smiggle, Peter Alexander, Just Jeans, and Dotti.

Smiggle has been the company’s stand out performer following its aggressive expansion overseas. Its expansion into the UK has been a great success, and helped the brand increase its year-over-year sales by 26%. The company plans to almost triple its store count in the UK within the next few years, so this growth is only just starting in my opinion.

The other key brand that I have previously picked out for international success is its nightwear retailer Peter Alexander. Its sales were up 22.5% year-over-year in the last half-year results and I feel quite sure this success could be replicated internationally.

Considering Smiggle and Peter Alexander operate on high margins, their strong performance will support the bullish view of analysts. They expect the company will grow its earnings by 19% per annum through to 2018, well ahead of the 10% per annum expected for the consumer discretionary industry as a whole.

The shares of Premier Investments don’t necessarily come cheap. They are priced at 25 times estimated forward earnings, compared to the consumer discretionary average of 21. But considering the superior growth prospects of Premier Investments I think they are worthy of this premium.

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Motley Fool contributor James Mickleboro has no position in any stocks mentioned. The Motley Fool Australia has no position in any of the stocks mentioned. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy. This article contains general investment advice only (under AFSL 400691). Authorised by Bruce Jackson.