While post-transitional societies have below replacement fertility, differentials exist with the lowest hovering around 1.0 and the highest remaining around replacement level. At present, the total fertility rate of 70% post-transitional countries (regions) is 1.5 and above, and only 8 countries (regions) have total fertility below 1.3. The differences of current social and economic development cannot fully explain the differences of post-transitional fertility level, and the answer need to be found from the historical process of social transition. Under the guidance of Ogben’s culture lag theory, this study proposes two concepts. One is the “Gender Equality Dilemma” and the other is the “Marriage and Fertility Cultural Conflict Dilemma”. These two concepts can basically explain the differences of post-transitional fertility level. China has now already been faced with these two “Dilemma”. In order to cope with the risk of low fertility, it is urgent to incorporate the concept of gender equality into the design of various public policies and realize the inclusiveness of fertility policies in an all-round and multi-level way.

The population theory of Marxism classic writers, represented by the principle of “Two Ways of Production”, scientifically interprets the universal development law of human society and fully embodies the fundamental concept of “Balance”. Accompanied by the hard explorations of China, the world's most populous country, Marxist view of balanced population has constantly realized innovation and development, and theories of balanced population with Chinese characteristics have been created to adapt Marxism to China's conditions. Especially in the New Era, it has been more profoundly expounded and more systematically explained, mainly reflected in Xi Jinping's population thoughts on promoting the long-term balanced population development to boost the great rejuvenation of the Chinese nation after the 18th National Congress of the Communist Party of China. Under the guidance of Marxist view of balanced population and its Chinization, China has creatively built a population system with Chinese characteristics and found a road of population development with Chinese characteristics.

Cohort-component method, the most widely used method in population projections, involves the issues of calculation and the details of programming when applied to the population projection software, which could impact the accuracy of projection results. Taking the mainstream projection software programs into account and based on the actual population data of Sweden, this paper, conducting comparative population projection tests, examines the applications of cohort-component method in the three population projection software programs including MORTPAK, Spectrum (DemProj) and PADIS-INT. The results show that the results of single-year age group obtained by the interpolation of five-year age group of the initial population are consistent and close between the three software programs; there is little difference in survival ratios calculated on the basis of the projection results of the three software programs; in the birth population projection, the three software programs don’t show great difference either. PADIS-INT has reached the projection level that international mainstream population projection software should have. Since PADIS-INT supports richer functionality especially in the parameter setting and the presentation of projection results, it is more suitable for a detailed population projection with application properties

 The implementation of the universal two-child policy will have a profound influence on China's future trends of population and changing path of aging. Using data from the 1% population sampling survey conducted by the National Bureau of Statistics in 2015，this paper conducts simulations of the size and structure of China's population over the years 2015-2100 by taking into account the potential demographic impacts of the fertility policy adjustment. The results show that China's total popula- tion will grow to the peak in around 2029 and then enter the era of negative population growth; China's population structure will be aging with shrinking working-age population size and expanding elderly population size; the speed of the decline in China's proportion of working-age population will be fast before 2050 and slow with fluctuations after 2050; China's size of elderly population will peak in around 2053 and then gradually begin declining; China will experience a rapid increase in proportion of elderly population before 2050 and the pace of population aging will slow down after 2050.

The numbers of accumulated couples and their extra births are major concerns after im- plementing the universal two-child policy．Using data from the 2014 national population sampling sur- vey，this paper，employing a population group-component calculation and projection method，provides estimates of the size of extra births that would be influenced by the two-child policy after computing the amount of accumulated couples in 2016．The results show that the number of target population under the two-child policy would be at around 91 million in 2016 among which women at age 40 and above account for 49． 6% ．Under medium fertility scenario，the size of extra births would reach around 17 mil- lion in 2017－2021 with an annual average number of 1．6－4． 7 million．Although the number of accu- mulated couples subject to the two-child policy is large，the size of their extra births would be relatively small，implying that China would have a smooth transition to the two-child policy．

How low is China’s recent total fertility rate? Data quality is the key to the answer． Population at ages 5 －7 from the 2015 household registration statistics is currently the latest available data which are believed to best represent the actual numbers of the 3 cohorts． Thus，estimates are highly reliable of China’s total fertility rates for 2008 to 2010 based on these data． The main conclusion is that China’s total fertility rates in 2008 － 2010 stood roughly at 1. 63 －1. 66. However，there is inevitable under －registration of the youngest age groups in the household registration data，fertility estimates provided in this paper are the lower limit of China’s actual fertility level． Thus，China’s total fertility rate in 2008，2009 and 2010 must be higher than 1．66，1．66 and 1. 63 respectively.

China has fully implemented a two-child fertility policy for couples that either side has no siblings. Meanwhile, two noticeable changes were observed in 2014. One was a noticeable fall in the sex ratio at birth, while the other was a marked increase of the number of annual births. In this context, this paper examines China’s current fertility by analyzing the effect of the new fertility policy and estimates fertility trends in the near future. Our analyses suggest that the new fertility policy has just had the effect that was previously expected, and China’s annual births would be expected to increase to nearly 18 million in 2015. China has not yet had the fertility “crisis”. With further adjustment of fertility policy, China’s fertility level still has potential to upturn and would rise to 1.7 or over in the very near future.