  The lifetimes of the first 2$^{+}$ states in the neutron-deficient
$^{76,78}$Sr isotopes were measured using a unique combination of the
$\gamma$-ray line-shape method and two-step nucleon exchange reactions at
intermediate energies. The transition rates for the 2$^{+}$ states were
determined to be $B$(E2;2$^{+}$$\to 0^{+}$) = 2220(270) e$^{2}$fm$^{4}$ for
$^{76}$Sr and 1800(250) e$^{2}$fm$^{4}$ for $^{78}$Sr, corresponding to large
deformation of $\beta_2$ = 0.45(3) for $^{76}$Sr and 0.40(3) for $^{78}$Sr. The
present data provide experimental evidence for mutually enhanced collectivity
that occurs at $N$ = $Z$ = 38. The systematic behavior of the excitation
energies and $B$(E2) values indicates a signature of shape coexistence in
$^{76}$Sr, characterizing $^{76}$Sr as one of most deformed nuclei with an
unusually reduced $E$(4$^{+}$)/$E$(2$^{+}$) ratio.
