Most countries have one city which is clearly top of the pops. In particular, one city (which may not necessarily be the national capital) is usually the largest population centre and the main economic powerhouse of a given country. Humbly presented here is a quick and not-overly-scientific list of ten countries that are an exception to this rule. That is, countries where two cities (or more!) vie neck-and-neck for the coveted top spot.
Note: all population statistics are the latest numbers on relevant country- or city-level Wikipedia pages, as of writing, and all are for the cities' metropolitan area or closest available equivalent.
There are several different ways of commonly identifying the "official centre point" of a city. However, there's little international consensus as to the definition of such a point, and in many countries and cities the definition is quite vague.
Most reliable and most common, is to declare a Kilometre Zero marker as a city's (and often a region's or even a country's) official centre. Also popular is the use of a central post office for this purpose. Other traditional centre points include a city's cathedral, its main railway station, its main clock tower (which may be atop the post office / cathedral / railway station), its tallest building, its central square, its seat of government, its main park, its most famous tourist landmark, or the historical spot at which the city was founded.
My home town of Sydney, Australia, is one of a number of cities worldwide that boasts most of the above landmarks, but all in different locations, and without any mandated rule as to which of them constitutes the official city centre. So, where exactly in Sydney does X mark the spot?