The one- and two-step mechanisms of the pd --> (HLambdaK+)-H-3 reactio
n in the range of incident proton kinetic energy T-p = 1.13-3.0 GeV ha
ve been investigated for the first time. A remarkable peculiarity of t
he two-step mechanism which incorporates subprocesses pp --> d pi(+) a
nd pi(+)n --> K(+)Lambda is the so-called velocity matching providing
the presence of all intermediate particles nearly to the on-mass-shell
. The differential cross section has been calculated using a realistic
model for the hypertritium H-3(Lambda) wavefunction. The maximum valu
e of the cross section is estimated as similar to 1 nb sr(-1). The con
tribution of the one-step mechanism with the elementary process pN -->
NK Lambda to the cross section has been found to be two to three orde
rs of magnitude smaller in comparison with the two-step mechanism.