They found that children who bully are at risk for engaging in more serious violent acts, like fighting frequently and carrying weapons.  For example, among boys surveyed who said they had bullied others at least once a week in school, 52.2 percent had carried weapons in the past month, 43.1 percent carried weapons to school, 38.7 percent fought frequently and 45.7 percent reported being injured in fights. The comparable statistics for boys who had never bullied others in school were 13.4 percent, 7.9 percent, 8.3 percent and 16.2 percent.  The greatest risk for engaging in violence-related acts was found among boys who bullied others when they were away from school; 70.2 percent of them had carried weapons.  Nor were girls exempt from potentially violent behavior. About 30 percent of girls who had bullied others in school at least once a week reported carrying weapons.  The victims of bullying were also at risk for violent behavior, with weapons carried by 36 percent of boys and 15 percent of girls who had been bullied in school at least once a week.  At greatest risk were boys and girls who both bullied others and were bullied themselves; they were 16 times as likely as youngsters not engaged in bullying behavior to carry weapons, the researchers reported last April in The Archives of Pediatric and Adolescent Medicine.  ''It appears that bullying is not an isolated behavior, but a sign that children may be involved in more violent behaviors,'' said Dr. Duane Alexander, director of the child health institute. ''The implication is that children who bully other children may benefit from programs seeking to prevent not just bullying, but other violent behaviors as well.''  Even preschoolers can be bullies, for example, giving other children insulting nicknames, refusing to invite particular classmates to birthday parties or excluding certain children from games.  In a study published in November in the journal Child Development, Dr. James Snyder of Wichita State University and colleagues reported that many kindergarten children found themselves verbally and physically abused by their playground peers. By the time the children reached first grade, an increasing amount of harassment had focused on a smaller group of perpetual victims.  In their observations of 266 students through two early grades, the Kansas researchers found that boys who experienced growing harassment were more likely to demonstrate antisocial and depressive behavior, and girls who were victimized in kindergarten were more likely to engage in antisocial behavior at home as they grew older and became more and more depressed at school if they continued to be victims.  ''Substantial rates of victimizations were observed,'' Dr. Snyder reported. ''On average, children were targets of peer physical or verbal harassment about once every three to six minutes.''  Another study of bullying among young adolescents, published in Pediatrics last month, emphasized the ''social plight of victims: they are not only targeted by bullies but also ostracized by many of their classmates.''  ''Victims suffer not only emotional distress but also social marginalization (i.e., classmates avoid them and they have low social status),'' Dr. Jaana Juvonen and colleagues at the University of California, Los Angeles, reported.  This study, unlike others that required children to report on their own bullying actions and instances of being bullied, questioned fellow students of sixth graders from 11 schools to determine the incidence and consequences of bullying and being bullied.  As in previous studies, they found that the most troubled group were those who were both bullies and victims. These youngsters exhibited the highest levels of social avoidance, conduct problems and school difficulties.  Furthermore, the researchers said, ''victims who bully others also best fit the profiles of seriously violent offenders.''  They analyzed 37 intended and actual school shootings and found that about two-thirds of those responsible had been bullied by their peers.  Parents are advised to ask children about teasing as early as age 5. If a child engages in bullying, he should be taught to apologize, ask forgiveness and shake hands. Older children who are teased can be taught not to play the role of victim, either by saying to the bully: ''I don't like your teasing. Stop it,'' or simply ignoring the bully and walking away.  Children who are bullied should not be blamed for being victims, nor should they be told to fight back. That can only worsen the problem, encouraging bullies to become increasingly hurtful. It is also important to boost victims' self-confidence and make sure they take part in activities they enjoy and can excel at. Also, parents who see bullying should teach their children to stick up for victims whenever possible.  Parents of bullies are advised to take the problem seriously, looking for the causes of anger or frustration, letting them know that hurtful behavior will not be tolerated, supervising their behavior more closely, ''punishing'' bullying with positive acts toward others and teaching nonviolent ways of solving problems.  Experts say that schools, communities and parents must collaborate to control bullying. One effective school-based program, covering kindergarten through fifth grade, is called Take a Stand, developed by Dr. Sherryll Kraizer. A set of teaching guides and a training videotape costs $195.
Jane E Brody Personal Health column describes widespread problem of bullying; Dr Tonja R Nansel and associates at National Institute of Child Health and Human Development conducted nationwide survey of 15,686 sixth-through tenth-grade students and found victims of bullying and bullies themselves are more likely to engage in more serious violent acts than those not involved in bullying; boys who bullied others away from school were shown to be at greatest risk for violence-related acts and likely to carry weapons; column holds that bullying can begin in preschool and gives suggestions on ways that parents can advise children on how to deal with bullies; drawing (M)