  The decay constants of pseudoscalar mesons are calculated in a relativistic
quark model which assumes that mesons are made of a valence quark antiquark
pair and of an effective vacuum like component. The results are given in terms
of quark masses and of some free parameters entering the expression of the
internal wave functions of the mesons. By using the pion and kaon decay
constants $F_{\pi^+}=130.7~MeV,~F_{K^+}=159.8~MeV$ to fix the parameters of the
model one gets $60~MeV\leq F_{D^+}\leq 185~MeV,~95~MeV\leq
F_{D_s}\leq230~MeV,~80~MeV\leq F_{B^+}\leq205~MeV$ for the light quark masses
$m_u=5.1~MeV,~m_d=9.3~MeV,~m_s=175~MeV$ and the heavy quark masses in the
range: $1.~GeV\leq m_c\leq1.6~GeV,~4.1~GeV\leq m_b\leq4.5~GeV$. In the case of
light neutral mesons one obtains with the same set of parameters
$F_{\pi^0}\approx 138~MeV,~F_\eta\approx~130~MeV,F_{\eta'} \approx~78~MeV$. The
values are in agreement with the experimental data and other theoretical
results.
