I'd put a coma after 'conditions', and probably change the phrase to 'in the current situation'. I'd use 'to manage'. Might would work beter IMO than may.
- In the modern conditions ensuring security depends on finding a way of management of policies of different counties worldwide with the view of locating emerging threats. New international institutes and modern methods may be used during this process.
countries' ?? governments' investments
- The speed with which information and money cross county’s borders erodes government’s capacity to control the country, with thousands of private sector investment causing sudden movements of capital and decline in prices.
speedy- too coloquial- rapid/instantaneous?
- Terrorists and drug traffickers use the latest speedy communications and information technology.
- Globalization makes it difficult to recognize emergent crises, which leads to the situation when a developing crisis is hard to notice and it is initially unclear what this crisis will lead to.