How can both life expectancy and death rate increase over 70 years time for a country? I see death rate and life expectancy for Greece.

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*For the first there is a constant growth from 1994 which is envisaged to grow up to 2068.

*For the latter there is a constant grown from 1950 which is envisaged to grow up to 2100

Can these diagrams coexist and yet be both realistic?
 A: They can definitely coexist, and are not mutually exclusive.
The U.N. definition of death rate is the proportion of your population dying every year (usually out of 1,000). Life expectancy is the average age at which the constituent population as a whole is expected to die.
So all that needs to happen is people to live longer on average than the previous generation (which they seem to be doing), and have a greater proportion of people dying every year than the year prior. Which can be sustained if each subsequent generation has an ever increasing population size compared to the generation before (which seems to be the case in the real world).

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*A really crude example:

Assume your population has $3$ constituents, Alice born in year $1$, and Bob and Clive born in year $2$.
If Alice was to have a life expectancy of $1$ year due to being born in an earlier generation with its disadvantages, and Bob and Clive were to have a life expectancy of $2$ years, as time passed from year $2$ to year $3$ you would observe Alice dying, your death rate increasing from $1/3$ to $1$ (the next year your whole population is expected to die), and your life expectancy increasing from $5/3$ to $2$.
