The process is used for suppressing the effect of signals that are received or sent via side lobes of an antenna (PA; HA) of an amplitude or phase monopulse radar device, in which for the purpose of position measurement of a first and, if need be, a second target (T1, T2) detected by the radar beam, three illumination functions Je(Lx), Jk(Lx) and Js(Lx) for the antenna (PA; HA) are provided for each measurement axis, as well as antenna functions Fe(X), Fk(X), and Fs(X) resulting from them. The first, second, and third illumination functions Je(Lx); Jk(Lx), and Js(Lx) are selected in this connection so that a quotient function Qe(X)=Fe(X)/Fs(X) or Qk(X)=Fk(X)/Fs(X), which is linearly or quadratically dependent on the target direction, is produced by normalizing the first and the second antenna functions Fe(X); Fk(X) with the third antenna function Fs(X). The power of this quotient is compared with at least one threshold value the or thk that is selected in accordance with the magnitude of the main antenna lobe, and when the threshold value the or thk is exceeded, the effect of the received signal is suppressed. In a preferred embodiment of the invention, the provision is made that the zero points of the antenna functions Fe(X), Fk(X), and Fs(X) are shifted slightly in relation to one another.