Ford Motor Company (NYSE:F) and General Motors Company (NYSE:GM) have built a sizable presence and following in India, which is the world's sixth-largest car market in the world.

Data provided by the Society of Indian Automobile Manufacturers, or SIAM, showed that car dispatches (units shipped from factories to dealers) declined for the first time in 11 years in 2013, by 9.6 percent to just over 1.8 million units, down from nearly 2 million units in the previous year.

Here's a look at some of the cars -- from two out of Detroit's Big Three automakers -- on display at the New Delhi auto show.

1. Ford Figo: The 5-door Figo hatchback seen here on display at the New Delhi auto show. Ford expects sales of compact cars, which is the most competitive segment in India, to grow from about 1 million units last year to roughly 2 million units in 2018 reflecting the significance of compact cars to Indian consumers. The base price of teh car, according to the company website, is just under 400,000 Indian rupees (about $6,400).

2. Ford EcoSport: Helping Ford India's sales numbers was its extremely popular Ecosport SUV, which reportedly logged thousands of orders in only a few days after its launch in 2013, and now has a waiting period of nearly a year. Ford, which uses India as an export hub, sold nearly 120,000 cars (including export units) in 2013 to clock 3 percent growth in a year that saw the overall market for passenger cars decline by nearly 10 percent.

3. Ford EcoSport: Yet another view of the SUV, which comes with a starting price tag of 620,000 rupees (about $10,000) while the top-end model can cost as much as $16,000. The company expects Asia Pacific to account for nearly a third of Ford’s global sales volume by 2015 -- up from 15 percent in 2010. 

4. Ford Figo Concept: Ford unveiled a new global concept sedan at the New Delhi auto show. The vehicle, at just under four meters in length is classified as a B-segment sedan and is eligible for certain tax rebates. And, according to a company statement, the concept provides a "glimpse into the kind of vehicle that Ford expects to play an important role in the region."

5. Ford Figo Concept: Yet another view of the concept sedan, which was launched in New Delhi just ahead of the auto show.

6. Ford Endeavour: This premium SUV now comes with an all-terrain edition, with prices starting at nearly $32,000. SUVs are growing in popularity in India as an upwardly mobile customer base prefers these sturdy vehicles to navigate the country's pot-holed urban roads and to take the family on a trip out of town.

7. Chevrolet Product Launch: Lowell Paddock, president and managing director of General Motors India, speaks to the media before the launch of its latest hatchback and a concept SUV. Paddock told International Business Times at the event that a turnaround in the industry could only be expected after India's national elections scheduled for mid-2014.

8. Chevrolet Beat and Chevrolet Adra: On Feb. 5, General Motors India launched a new version of the Chevrolet Beat, which is the company's best-selling model in the cost-conscious entry segment of the Indian car market. The company also unveiled a concept SUV aimed at the growing demand for crossover vehicles in the country.

9. Chevrolet Trailblazer: The Trailblazer on display at the New Delhi auto show. This vehicle, slotted in the premium SUV segment, starts at a price tag of about $26,000.

10. Corvette Stingray: GM also showcased the Stingray at the New Delhi auto show, which reportedly would begin with a base price of about $81,000.

11. Chevrolet Beat: The latest version of GM's best-selling small car, which was launched last week at the New Delhi auto show, will be offered at a base price of just over 400,000 rupees, or $6,500.

12. Chevrolet Sail-UVA in Manchester United colors: GM unveiled its special edition Chevrolet Beat and Chevrolet SAIL U-VA at the New Delhi auto show. British football club Manchester United, which has a huge fan following in India, is Chevrolet's official automotive partner.