We present an estimation of the expected number of arcs and arclets in a su
rvey of nearby (z < 0.1) clusters of galaxies, which takes into account the
observational constraints. We show that strong lensing effects are not com
mon, but also that they are not as rare as usually stated. Indeed, for a gi
ven cluster, the predicted number of arcs strongly depends on the magnitude
limit of the survey and the actual value of the seeing. We also describe t
he procedures and results of a search for gravitational arcs and arclets in
a sample of 33 galaxy clusters, representative of the local cluster distri
bution and spanning the redshift range of 0.014 < z < 0.076. Only one new a
rc candidate was discovered, located <similar to> 3 arcmin away from the ce
nter of the cluster Abell 3266 (z = 0.059), whose redshift was found to be
z = 0.073. The assumption that a mass concentration around a bright cluster
elliptical away from the arc candidate could 16."6 explain this arc as a g
ravitational image requires the presence of a very massive substructure in
this cluster (M/L-V similar to 163 M./L.). Although such substructure canno
t be completely discarded, the nature of the arc candidate most possibly co
rresponds to a disk galaxy belonging to A3266. Our simplified theoretical m
odel predicts that the probability of finding at least one gravitational ar
c in the sample investigated is 25%, in good agreement with the actual numb
er of arcs found, N = 1 or 0, either adopting the arc in A3266 as a gravita
tional image or not. We conclude that a deep survey of the central regions
of low-z galaxy clusters, with very good image quality, should allow signif
icant progress in the mapping of their central mass concentration.